The 21-nation Asia-Pacific Economic Cooperation forum brought Mr. Obama to Singapore, but he is focusing on individual meetings Sunday with Medvedev and with Indonesia's Susilo Bambang Yudhoyono, president of the world's largest Muslim nation (and the president's home as a boy). The U.S.-Russia meeting takes place as the nations seek a successor to a Cold War-era agreement.
President Obama also planned another milestone: joining a larger meeting that includes the leader of military-ruled Myanmar. Mr. Obama is sure to face criticism at home, particularly from conservatives, for doing so - a significant step up in his administration's new policy of "pragmatic engagement" that is a shift from years of U.S. isolation and sanctions.
President Obama and Medvedev agreed in April to reach a new nuclear arms reduction treaty to replace Strategic Arms Reduction Treaty 1 before it expires on Dec. 5. Later, in Moscow in July, they agreed further to cut the number of nuclear warheads each nation possesses to between 1,500 and 1,675 within seven years.
U.S. officials say that the two nations now have agreed on the broad outlines of a new treaty, with the expectation that the leaders will sign one during President Obama's travels to Europe in early December to accept the Nobel Peace Prize.
Such an agreement would be a big feather in President Obama's cap and bragging rights toward his promise to work toward a nuclear-free world, offering momentum for other arms-control and nonproliferation efforts. The president has been hinting at his optimism on the issue leading up to and during his Asia trip.
"We are already taking steps to bring down our nuclear stockpiles in cooperation with the Russian government," he said during a news conference in Japan with Prime Minister Yukio Hatoyama.
A new treaty also could boost relations with Russia at a time that Washington is looking for its cooperation on issues including reining in Iran's nuclear ambitions.
Negotiators already have worked through a number of contentious issues and agreed on the number of warheads, the number of delivery systems and what will count as a delivery system, officials said.
The remaining issues in negotiations involve procedures for the two countries to verify that the other side is meeting the terms of the treaty, two administration officials said speaking on condition of anonymity because of the sensitivity of the negotiations.
"I don't foresee a major problem that can't be resolved within the next four weeks," said Daryl Kimball, executive director of the Arms Control Association, which follows the negotiations. "Neither side wants to go without a new agreement for very long."
Ben Rhodes, deputy national security adviser to President Obama, suggested it wasn't likely the leaders would announce a breakthrough but that holding talks at such a high level while they are going on could help bring one about.
The existing START treaty, signed by Soviet President Mikhail Gorbachev and President George H.W. Bush in 1991, led each country to cut its nuclear warheads by at least one-quarter, to about 6,000. In 2002, Presidents Vladimir Putin and George W. Bush signed the Treaty of Moscow, which specified further cuts to between 1,700 and 2,200 operationally deployed warheads by 2012.
The U.S. now has about 2,200 such warheads deployed, compared to about 2,800 for the Russians.
Once a deal is signed, it still would need ratification by the Russian Duma and the U.S. Senate to take effect.
Myanmar, also known as Burma, is a member of the 10-nation Association of Southeast Asian Nations, or ASEAN, and President Obama is sitting in on their summit. A U.S. president has never met with a leader of the Burmese junta, one of the world's worst human-rights offenders.
Despite the new engagement, the Obama administration has said that sanctions will not be lifted unless Burma's rulers make democratic progress, such as releasing opposition leader Aung San Suu Kyi, a Nobel Peace Prize laureate and democracy icon who has been under house arrest for most of the last two decades.
Obama aides as well as outside Asia experts have defended the administration's new gamble on Burma, even while admitting it may not succeed.
"One definition of insanity is to do the same thing over and over and expect a different outcome," said Jeffrey Bader, President's Obama's top Asia adviser.
By AP White House Correspondent Jennifer Loven; AP writers Desmond Butler in Washington and Vijay Joshi in Singapore contributed to this report