The United States and the Soviet Union resumed their elusive search for a nuclear arms agreement here today, meeting for mroe than two hours in a session domianted by Soviet leader Mikhail Gorbachev's proposal to eliminate nuclear weapons by the end of the century.

Today's session was the first since Gorbachev and President Reagan agreed at their summit meeting here last November to accelerate the pace of negotiations.

The mood was noticeably upbeat inside the Soviet mission where the meeting was held and Moscow's chief negotiator, Victor Karpov, greeted the leader of the U.S. delegation, Max Kampelman, at the door with a broad smile.

Kampelman told Karpov that the U.S. delegation was anxious to reach agreements to remove the threat of nuclear war.

Karpov predicted that Gorbachev's proposed three-step timetable for elimination of all nuclear weapons by the year 2000 would be central to the negotiations.

In his remarks before the session, Karpov stressed the apparent change in the Soviet position on the French and British nuclear arsenals.

"We, as part of the first stage of delivering the world from nuclear weapons, agree that we can get rid of American and Soviet missiles in Europe," Karpov said.

The Gorbachev initiative calls for freezing British and French weapons at a time when both countries are expanding their nuclear arsenals.

Karpov had tough words for Reagan's Strategic Defensive Initiative, but said again that SDI research would not block an agreement on intermediate-range missiles.