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President Obama and President Dimitri Medvedev of Russia expressed dissatisfaction Sunday with Iran’s response to a nuclear offer made by world powers, raising the prospect that sanctions may be the next step in the West’s ongoing efforts to rein in Tehran’s nuclear ambitions.

The two men, meeting during an Asia-Pacific summit conference in Singapore, also made progress in efforts to negotiate a replacement for a key arms control treaty between the United States and Russia that is set to expire in December, U.S. administration officials said.

While White House officials acknowledged on Sunday that a new pact to replace the Strategic Arms Reduction Treaty, or START, will be ratified soon, they said they expect to reach a “bridge” agreement that will preserve the...