A Kremlin statement said Obama and Medvedev "expressed the determination to create constructive and positive interaction for the good of global stability and development" and agreed that their countries had a common responsibility to address "serious problems of a global nature."
To that end, according to the Kremlin statement, Medvedev and Obama believe an "early bilateral meeting" should be arranged.
Obama's office did not issue a statement describing the call.
A Bush administration plan for setting up a missile shield close to Russia's borders has been a sore point with the Kremlin and has served as another dent in its battered relationship with the U.S.
On Wednesday, the day after Obama's election, Medvedev threatened to move short-range missiles to Russia's borders with NATO allies even as the U.S. offered new proposals on nuclear arms reductions as well as missile defense. Allowing Russian observers at planned missile defense sites in Poland and the Czech Republic were among them, U.S. officials said.
During the presidential campaign, Obama expressed skepticism about the system, saying that it would require much more vigorous testing to ensure it would work and justify the billions of dollars it would cost.
Obama foreign policy adviser Denis McDonough said Saturday that Obama had "a good conversation" with Polish President Lech Kaczynski about the American-Polish alliance but that Obama had made no commitment on the missile shield plan.
"His position is as it was throughout the campaign, that he supports deploying a missile defense system when the technology is proved to be workable," McDonough said.
That was in contrast to a statement issued by the Polish president. Kaczynski said Obama "emphasized the importance of the strategic partnership of Poland and the United States and expressed hope in the continuation of political and military cooperation between our countries. He also said that the missile defense project would continue."
President Bush wanted construction of a European missile shield -- installations would be in Poland and the Czech Republic -- to begin before he left office in January with a completion date of 2012. Experts in the Defense Department believe more intercep
tor testing is required, according to reports over the summer. Additional tests could delay the program for years.
In Madrid, Spanish Prime Minister Jose Luis Rodriguez Zapatero told reporters Saturday that he had spoken by telephone with Obama and that they discussed their desire to meet each other and work together, though no concrete plans were made.
"We had a very, very cordial conversation," Zapatero said.
On another international matter, Obama's office had little to say in response to a statement by Khaled Mashaal, leader of the Palestinian militant group Hamas, that he is ready to talk to Obama "with an open mind." The exiled militant leader told Sky News from Damascus, Syria, that the election of an American president with African roots is "a big change."
McDonough said, "President-elect Obama said throughout the campaign that he will only talk with Hamas if it renounces terrorism, recognizes Israel's right to exist, and agrees to abide by past agreements."
The Bush administration has boycotted Hamas, as has most of the international community, because Hamas refuses to renounce violence or recognize Israel.