The plan, which Fox News has learned was agreed to in principle during negotiations, would constitute the most intrusive weapons inspection program the U.S. has ever accepted.
Foreign Minister Sergey Lavrov, who met with Secretary of State Hillary Clinton, said publicly Tuesday that the two nations have made "considerable" progress toward reaching agreement on a new strategic arms treaty.
The 1991 Strategic Arms Reduction Treaty, or START, expires in December and negotiators have been racing to reach agreement on a successor.
Clinton said the U.S. would be as transparent as possible.
"We want to ensure that every question that the Russian military or Russian government asks is answered," she said, calling missile defense "another area for deep cooperation between our countries."
On another critical issue, Lavrov declared that it would be counterproductive to threaten Iran with more sanctions over its nuclear program -- as he resisted efforts by Clinton to win agreement for tougher measures should Iran fail to prove its program is peaceful.
Clinton visited Moscow on her first trip since becoming America's top diplomat, in an effort to gauge Moscow's willingness to join the U.S. in imposing sanctions.
Clinton said the U.S. agreed it was important to pursue diplomacy with Iran.
"At the same time that we are very vigorously pursuing this track, we are aware that we might not be as successful as we need to be, so we have always looked at the potential of sanctions in the event we are not successful and cannot assure ourselves and others that Iran has decided not to pursue nuclear weapons," she said at a joint news conference.
Iran insists it has the right to a full domestic nuclear enrichment program and maintains it is only for peaceful purposes, such as energy production.
President Obama -- who visited Russia in July -- has vowed to "reset" U.S.-Russia relations. On Tuesday, Clinton apologized for missing that meeting because of a broken elbow.
"But now both my elbow and our relationships are reset and we're moving forward, which I greatly welcome," she said.
She was to meet with Russian President Dmitry Medvedev later Tuesday.
Fox News' Dana Lewis and The Associated Press contributed to this report.