BBC
The area has suffered heavy bombardment by government forces in recent weeks.
The rebel Free Syrian Army (FSA) said on Thursday it was leaving the district in a "tactical withdrawal".
The FSA said 4,000 civilians had refused to leave their homes and it was withdrawing to save them from an all-out assault.
Of the 100,000 people who normally live in Baba Amr, only a few thousand remain.
'Extremely worrying' It has been snowing heavily in Homs, slowing the advance of government troops who began an offensive on Tuesday, but also worsening conditions for civilians.
"We know the humanitarian situation on the ground is extremely worrying," she added.
Meanwhile, France says two French journalists who had been trapped in Homs are now safely out of the country.
Reporter Edith Bouvier, 31, and photojournalist William Daniels, 34, are now in Lebanon, French President Nicolas Sarkozy told a news conference on Thursday.
Ms Bouvier was badly injured in the bombardment of a makeshift media centre last week, in which two journalists were killed and another one wounded.
"I have just spoken to Edith Bouvier, who is naturally very tired, who has suffered a great deal, but who is happy to be free and will be treated soon," he said. "I want to thank all those who contributed to this happy outcome."
Unconfirmed reports say the bodies of two Western journalists killed in the same attack, Marie Colvin of Britain's Sunday Times and French photojournalist Remi Ochlik, have been found.
Video footage posted on the internet purported to show both bodies being buried by activists in Homs.
Split opposition? In a unanimous statement on Thursday, the UN Security Council expressed its "disappointment" that UN humanitarian chief Valerie Amos had not been granted authorisation to visit Syria, and demanded immediate access for her.
Russia and China, who vetoed two previous Security Council resolutions on Syria, also backed the call.
The council's 15 member countries also said that they "deplore" the deteriorating situation, "in particular the growing number of affected civilians, the lack of safe access to adequate medical services, and food shortages, particularly in areas affected by fighting and violence such as Homs, Hama, Deraa, Idlib".
The members urged Syrian authorities to grant "immediate, full and unimpeded access" to aid agencies.
The UN estimates more than 7,500 people have died in an 11-month anti-government uprising in Syria.
The Local Co-ordination Committees, a network of activists, says 33 people died on Thursday, including 21 in Homs. Their figures cannot be verified independently.
The exile political opposition Syrian National Council (SNC) says it has formed a military bureau to co-ordinate the various armed anti-government groups.
Announcing the creation of the new bureau, SNC leader Burhan Ghalioun said the uprising had begun as a non-violent movement, but the council had to "shoulder its responsibilities in light of this new reality".
Mr Ghalioun said the bureau would function like a defence ministry and would be staffed by soldiers from the FSA as well as civilians.
However, the head of the FSA, Col Riyad al-Asaad, has said his organisation will not co-operate with the new bureau, our correspondent says.
An activist in the Syrian city of Homs has said the Free Syrian Army has left the embattled district of Baba Amr
The Red Cross is due to enter the Baba Amr district of the Syrian city of Homs on Friday to deliver food and medical supplies after a month-long siege.
The International Committee of the Red Cross (ICRC) is to enter the area with the Syrian Red Crescent, and is also planning to evacuate the wounded.The area has suffered heavy bombardment by government forces in recent weeks.
The rebel Free Syrian Army (FSA) said on Thursday it was leaving the district in a "tactical withdrawal".
The FSA said 4,000 civilians had refused to leave their homes and it was withdrawing to save them from an all-out assault.
Of the 100,000 people who normally live in Baba Amr, only a few thousand remain.
'Extremely worrying' It has been snowing heavily in Homs, slowing the advance of government troops who began an offensive on Tuesday, but also worsening conditions for civilians.
Continue reading the main story 
The announcement in Paris by the Syrian National Council (SNC) that it is setting up a new "military bureau" to coordinate and funnel arms and support to the Free Syrian Army (FSA) has exposed a glaring rift in opposition ranks.
SNC President Burhan Ghalioun, said that the commander of the FSA, Col Riyad al-Asaad, and Gen Mustafa al-Shaikh, who recently set up a "Supreme Military Council", were on board the project.
But Col Asaad told al-Jazeera that he had spoken to Mr Ghalioun the night before, that they had differed, and failed to reach agreement.
He said the FSA had its own military strategy, did not want political interference, and would not coordinate with the SNC and its new military bureau.
He had earlier criticised the SNC for failing to do anything practical to help people inside Syria. But with an Arab League resolution in January now providing political cover for countries like Saudi Arabia and Qatar which want to arm the opposition, it's not clear why Col al-Asaad is rejecting the proffered largesse.
While it is very hard to assess the true strength of the FSA and the level of popular support it enjoys inside Syria, it is frequently named in slogans chanted at anti-regime demonstrations, and many activist videos posted on the internet have shown military defectors declaring their allegiance to the FSA.
Analysis
SNC President Burhan Ghalioun, said that the commander of the FSA, Col Riyad al-Asaad, and Gen Mustafa al-Shaikh, who recently set up a "Supreme Military Council", were on board the project.
But Col Asaad told al-Jazeera that he had spoken to Mr Ghalioun the night before, that they had differed, and failed to reach agreement.
He said the FSA had its own military strategy, did not want political interference, and would not coordinate with the SNC and its new military bureau.
He had earlier criticised the SNC for failing to do anything practical to help people inside Syria. But with an Arab League resolution in January now providing political cover for countries like Saudi Arabia and Qatar which want to arm the opposition, it's not clear why Col al-Asaad is rejecting the proffered largesse.
While it is very hard to assess the true strength of the FSA and the level of popular support it enjoys inside Syria, it is frequently named in slogans chanted at anti-regime demonstrations, and many activist videos posted on the internet have shown military defectors declaring their allegiance to the FSA.
Many of those still in Baba Amr are without power and running low on basic supplies.
"We fear there are many people who are seriously wounded [in Baba Amr]," ICRC spokeswoman Carla Haddad Mardini told the BBC on Thursday."We know the humanitarian situation on the ground is extremely worrying," she added.
Meanwhile, France says two French journalists who had been trapped in Homs are now safely out of the country.
Reporter Edith Bouvier, 31, and photojournalist William Daniels, 34, are now in Lebanon, French President Nicolas Sarkozy told a news conference on Thursday.
Ms Bouvier was badly injured in the bombardment of a makeshift media centre last week, in which two journalists were killed and another one wounded.
"I have just spoken to Edith Bouvier, who is naturally very tired, who has suffered a great deal, but who is happy to be free and will be treated soon," he said. "I want to thank all those who contributed to this happy outcome."
Unconfirmed reports say the bodies of two Western journalists killed in the same attack, Marie Colvin of Britain's Sunday Times and French photojournalist Remi Ochlik, have been found.
Video footage posted on the internet purported to show both bodies being buried by activists in Homs.
Split opposition? In a unanimous statement on Thursday, the UN Security Council expressed its "disappointment" that UN humanitarian chief Valerie Amos had not been granted authorisation to visit Syria, and demanded immediate access for her.
Russia and China, who vetoed two previous Security Council resolutions on Syria, also backed the call.
The council's 15 member countries also said that they "deplore" the deteriorating situation, "in particular the growing number of affected civilians, the lack of safe access to adequate medical services, and food shortages, particularly in areas affected by fighting and violence such as Homs, Hama, Deraa, Idlib".
The members urged Syrian authorities to grant "immediate, full and unimpeded access" to aid agencies.
How Syrian activists have become citizen journalists
The Local Co-ordination Committees, a network of activists, says 33 people died on Thursday, including 21 in Homs. Their figures cannot be verified independently.
The exile political opposition Syrian National Council (SNC) says it has formed a military bureau to co-ordinate the various armed anti-government groups.
Announcing the creation of the new bureau, SNC leader Burhan Ghalioun said the uprising had begun as a non-violent movement, but the council had to "shoulder its responsibilities in light of this new reality".
Mr Ghalioun said the bureau would function like a defence ministry and would be staffed by soldiers from the FSA as well as civilians.
However, the head of the FSA, Col Riyad al-Asaad, has said his organisation will not co-operate with the new bureau, our correspondent says.