Armenian President Serzh Sargsyan and Azeri President Ilham Aliyev signed the largely symbolic document at Medvedev's Maiendorf residence, just outside Moscow on Saturday.
Armenia has traditionally been a staunch ally of Russia, while energy-rich Azerbaijan has maintained friendly ties with Georgia, but Moscow has been looking for greater cooperation with Azerbaijan on energy issues.
The five-point document, published on the Kremlin's web site, says both countries will step up efforts to find a peaceful solution over Nagorno-Karabakh, an ethnic Armenian enclave inside Azerbaijan that broke away after a bloody conflict in the early 1990s that killed more than 30,000 and displaced more than 1 million.
The declaration is the first such document signed by the heads of the two states since Russia mediated a cease-fire agreement in 1994.
While it stresses the need for a political settlement based on international law, the document does not contain any significant commitments, such as to forego the use of force, nor does it mention the conflicting issues at the heart of the conflict, territorial integrity and national self-determination.
The outcome of the meeting was not as significant as some may have hoped.
"This was not much different than dozens of meetings before," Svante Cornell, research director at the Central Asia-Caucasus Institute, a joint U.S.-Swedish think tank, said Tuesday by telephone from Tbilisi, Georgia. "All we have seen is basically two leaders committing themselves to solving the conflict."
Alexei Malashenko, an analyst with the Moscow Carnegie Center, said the declaration was largely ceremonial.
"The fact that Medvedev [presided over the talks) just means that both sides accept Russia as mediator," Malashenko said Tuesday. "Russia needed an urgent rehabilitation as peacekeeper in the region."
Moscow's relations with the West worsened dramatically after it sent soldiers and tanks deep into Georgia to repel a Georgian military attack to reclaim its breakaway region of South Ossetia in August.
The declaration also says negotiations should continue within the framework of the so-called Minsk Group, a 12-member body headed jointly by Russia, France and the United States, and overseen by the Organization for Security and Cooperation in Europe.
U.S. Deputy Assistant Secretary of State Matthew Bryza and French Ambassador Bernard Fassier were at Maiendorf, an OSCE spokesman said by telephone from Vienna.
Bryza, the senior U.S. diplomat overseeing the South Caucasus region, praised the result.
"My country fully supports this document. The declaration shows that both presidents can work seriously towards solving this conflict," he said, Interfax reported Monday.
Cornell said the declaration was a show of force by the Kremlin capitalizing on the weakness of the West, as the Georgian war in August, the global financial crisis and the leadership change in the United States would all work to cripple Western influence in the region.
"There is a new geopolitical situation now," he said.
Russia, he said, was offering a solution that would mean a loss of independence for Azerbaijan, possibly through the deployment of a Moscow-sponsored peacekeeping force on its territory.
Cornell said Moscow was probably eyeing a "common state" solution, something that had been on the negotiating table back in the 1990s.
This proposal, which had been rejected by Baku, focuses on bringing Azerbaijan and Nagorno-Karabakh together in a confederation.
Carnegie's Malashenko said that while its influence in the region has grown, Russia would not go it alone.
"To solve this conflict, you need more than one mediator; you need a group of mediators," he said. "Moscow won't act outside the format of the Minsk Group."
Malashenko also denied that the talks might herald a weakening of Moscow's traditional support for Armenia.
"I cannot imagine that one country will give one-sided support to one party, because this is impossible," he said.
Both Azerbaijan and Armenia depend on trade routes through Georgia.
Moscow has recently been courting Azerbaijan, which wants to sell more gas to Russia.
Medvedev signed a cooperation agreement with Aliyev in Baku in July, and in Moscow this September both leaders discussed direct talks between Azerbaijan and Armenia over Nagorno-Karabakh.
Europe has also been making overtures to Azerbaijan as a vital supplier to a proposed new gas pipeline, which would reduce Western dependence on Russian energy.
The Nabucco pipeline project has been backed both by the European Union and the United States.
EU Energy Commissioner Andris Piebalgs will travel to Turkey and Azerbaijan this Wednesday to show Europe's commitment to the project, The Associated Press reported.
Moscow has worried the EU by negotiating with Turkmenistan and Kazakhstan to commit to sending their Caspian Sea gas through Russia.
It is also pushing South Stream, a rival pipeline project by state-controlled Gazprom, which is slated to cost some $13 billion.
A Message from The Moscow Times:
Dear readers,
We are facing unprecedented challenges. Russia's Prosecutor General's Office has designated The Moscow Times as an "undesirable" organization, criminalizing our work and putting our staff at risk of prosecution. This follows our earlier unjust labeling as a "foreign agent."
These actions are direct attempts to silence independent journalism in Russia. The authorities claim our work "discredits the decisions of the Russian leadership." We see things differently: we strive to provide accurate, unbiased reporting on Russia.
We, the journalists of The Moscow Times, refuse to be silenced. But to continue our work, we need your help.
Your support, no matter how small, makes a world of difference. If you can, please support us monthly starting from just $2. It's quick to set up, and every contribution makes a significant impact.
By supporting The Moscow Times, you're defending open, independent journalism in the face of repression. Thank you for standing with us.
Remind me later.