At a joint news conference with Gottemoeller at the US embassy in the Italian capital, Antonov said: "We are sure, that this treaty, new treaty, will help to improve relations between [the] United States and [the] Russian Federation."
An arms reduction deal is seen by both sides as a way to show that the former Cold War foes can work together despite rows on other issues, such as Nato expansion into regions once dominated by Moscow and how to approach Iran's nuclear programme.
Gottemoeller said: "These negotiations will be very important in hitting the reset button in the US-Russian relationship, restoring mutual confidence to make progress in a lot of areas."
From now on, US and Russian negotiators will meet regularly, and Start-1 will be discussed at a May meeting between Sergei Lavrov, the Russian foreign minister, and Hillary Clinton, the US secretary of state.
Signed in July 1991, Start-1 placed limits on the number of missiles and warheads that Moscow and Washington could have, leading to steep reductions in the nuclear arsenals of both sides. Start-1 expires in December.
Talks on replacing the treaty, seen as a cornerstone of strategic arms control, made little progress under George Bush, Obama's predecessor.
Andrei Nesterenko, a Russian foreign ministry spokesman, also said Moscow welcomed Obama's statement that the president would seek senate ratification of the Comprehensive Nuclear Test Ban Treaty, which would place a broad ban on nuclear explosions for testing purposes.
"We welcome Mr Obama's work toward the ratification of this agreement," he said.