 Mr Medvedev is holding talks with the leaders of Russia's Caucasus republics |
Russia's president has made a surprise visit to Dagestan, a day after 12 people were killed in a double suicide attack in the North Caucasus republic.
Dmitry Medvedev called for "tough, severe and preventative" anti-terrorism tactics at talks with regional leaders. Funerals are meanwhile being held in Moscow for most of the 39 people killed on Monday when two suicide bombers blew themselves up on the city's Metro.
A rebel Chechen leader, Doku Umarov, has said he ordered the attack.
In a video message posted on a rebel website, he purportedly said they were carried out to avenge the killings of Chechens by federal security forces in February, and warned Russians to prepare for more.
Investigators had already said they believed the women who blew themselves up in Moscow were linked to North Caucasus militants.
'Punish'
Accompanied by top security officials, President Medvedev flew to Makhachkala on Thursday to hold emergency talks with the leaders of Russia's troubled North Caucasus republics, including Dagestan, Chechnya and Ingushetia.
"We must deal sharp dagger blows to the terrorists; destroy them and their lairs," Mr Medvedev said.
 |   All of these [bombings] are links of the same chain  Russian President Dmitry Medvedev  |
"We have ripped the heads off the most infamous bandits, but it appears that this was not enough. We will track them all down in due time and will punish them all, just as we did to the previous ones. We will act only this way."
His visit comes a day after 12 people, nine of them police officers, were killed in two suicide bombings in the Dagestani town of Kizlyar, not far from the border with Chechnya.
In the first blast, a man detonated about 200kg of explosives when police tried to stop his car near the offices of the local interior ministry and the domestic intelligence agency, the Federal Security Service (FSB).
As police, emergency services personnel and residents gathered at the scene, another man wearing a police uniform approached and blew himself up, killing among others the town's chief of police.
Overnight, two people were killed when their car, thought to be packed with explosives, blew up in the west of Dagestan.
Mr Medvedev told security officials on Tuesday that the bombings in Kizlyar and Moscow were "links of the same chain".
"This is the manifestation of the same terrorist activity which has lately begun to make itself felt in the Caucasus, which we are all fighting against and which we will continue to fight," he added.
The attacks came almost a year after President Medvedev declared an end to Russia's "counter-terrorism operations" in Chechnya, in a bid to "further normalise the situation" after 15 years of conflict that claimed more than 100,000 lives and left it in ruins.
Despite this, the mainly Muslim republic continues to be plagued by violence, and over the past two years Islamist militants have stepped up attacks in neighbouring Ingushetia and Dagestan.
'Not the last'
In the video published on the rebel Kavkaz Center website, a man claiming to be Chechen rebel leader Doku Umarov said his group was responsible for the two suicide bombings that struck Moscow's Metro.
Doku Umarov: 'I promise you that the war will come to your streets'
He said the attacks were an act of revenge for the killings of Chechen and Ingush civilians by the Russian security forces near the town of Arshty on 11 February.
"These people were mercilessly eliminated, murdered by these bandit groups carrying the name of the FSB. Their bodies had stab wounds and were insulted."
The rebel, who styles himself as the Emir of the Caucasus Emirate, said attacks on Russian soil would continue.
"I promise you that the war will come to your streets, God willing, and that you will feel it in your own lives and on your own skin," he warned Russian citizens in the video, which he said had been recorded on Monday - just hours after the Metro attacks.
The BBC's Richard Galpin in Moscow says this is exactly what many people there had feared after the bombings.
They showed how vulnerable the capital is to this kind of attack and that the intelligence agencies lack the information they need to protect the city and its population, our correspondent says.
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