It is believed flight MH17 crashed after being hit by a surface-to-air missile fired from a rebel-held area in east Ukraine.
The plane crashed on Thursday, killing all 298 people on board.
The Boeing 777 was flying from Amsterdam to Kuala Lumpur. It fell between Krasni Luch in Luhansk region and Shakhtarsk in the neighbouring region of Donetsk.
Latest figures released by Malaysia Airlines show the plane was carrying 189 Dutch nationals, 27 Australians, 44 Malaysians (including 15 crew), 12 Indonesians and 10 Britons, as well as a number of other nationalities.
'Intoxicated guard' Michael Bociurkiw, a member of the OSCE team, said their access had been limited despite assurances from the regional rebel commander that they would be allowed into the site.
"A visibly intoxicated armed guard fired his rifle in the air when one of the observers walked out of the prescribed area," Mr Bociurkiw told journalists.
Several bodies had been marked but left exposed to the elements, Mr Bociurkiw said, and rescue workers were unable to indicate whose responsibility it would be to remove them.
Thomas Greminger, the Swiss chairman of the OSCE's permanent council, told the BBC they would continue to work to see that an international investigation could take place.
The UN Security Council has called for a full and independent international investigation into what happened to the aeroplane.
The two sides in the Ukrainian conflict have accused each other of shooting it down.
Ukraine's government called the disaster an "act of terrorism" and released what they say are intercepted phone conversations that proved the plane was shot down by separatists.
But the pro-Russian separatists said a Ukrainian air force jet had brought down the airliner.
He described it as "an outrage of unspeakable proportions", saying he would ensure "the truth is out".
Mr Obama said it was up to Russia to stop the flow of heavy armaments and fighters into Ukraine.
Yuriy Sergeyev, Ukraine's ambassador to the UN, said the attack would not have been possible if Russia "did not provide sophisticated anti-aircraft missile systems" to rebels.
But Russia denies supporting the separatists and Foreign Minister Sergey Lavrov dismissed claims that the country was connected to the attack.
"Regarding those claims from Kiev that we allegedly did it ourselves: I have not heard a truthful statement from Kiev for months," he told a Russian TV news channel.
Russian President Vladimir Putin said the crash was a "tragedy". He also called for a ceasefire and peace talks, but fresh clashes were reported on Friday less than 100km (60 miles) from the crash site.