The decision was made during talks between Russian Prime Minister Sergei Stepashin and Vice President Al Gore, co-chairmen of a U.S.-Russia commission.
But Gore, at a news conference, said a START III treaty would not be signed until the Russian parliament ratifies the 1993 START II accord.
Despite repeated assurances by Russian President Boris Yeltsin that he would push the treaty, it has been stalled by objections from nationalists and communists, as well as concern the pact would put Russia at a disadvantage unless it builds costly new weapons.
Even so, Stepashin told reporters, "we will try to get START II ratified in the fall."
Gore said prompt action was unlikely in the aftermath of tensions over Kosovo. But he acknowledged, "That cannot explain the long delay."
"We are entering the 21st century. We have to enter it as friends," said Stepashin, whose visit was aimed at putting U.S.-Russian relations on an even course after an angry rift over NATO's bombing of Yugoslavia. "We have to understand each other. We have to respect each other."
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In the same vein, Gore said in a statement, "In this new era, strong U.S.-Russia ties will be an essential component of American national security and global stability."
On a touchy front, Gore and Stepashin reluctantly acknowledged they discussed the number of Russian spies in the United States. The Washington Times, in a front-page article on Monday, said the United States was insisting on a sharp reduction.
"Old attitudes fade away very slowly," Gore said, referring, apparently, to large Cold War-era spy contingents.
Stepashin, who had refused on Monday to respond to a question about spies, said, "As long as states exist there will always be special services."
Gore said Sandy Berger, President Clinton's national security assistan, and Vladimir Putin, Berger's Russian counterpart, will take up the matter in private discussions.
In 1993, the United States and Russia agreed to shrink their arsenals of long-range nuclear warheads so that neither side would have more than 3,500. But the Russian legislature has refused to ratify the accord.
Prime Minister Sergei Stepashin
The actions in the arms control arena were not big steps, but they represented an effort to work together, at least in areas of mutual interest.
Under START III, arsenals would be cut to between 2,000 to 2,500 warheads each.
Stepashin, in his first U.S. visit since becoming prime minister, sought to convince American investors that Russia is where they should seek their fortunes. He also wanted to repair a rift over NATO's bombing of Yugoslavia in the spring, a strategy bitterly opposed by Russia. It forced Serb troops to quit Kosovo, though, and Russian peacekeeping troops are on duty in the province along with U.S. and other NATO forces.
Stepashin said Yeltsin would continue the effort at a September meeting with Clinton in New Zealand at a conference of Asian and Pacific nations.
Still reflecting a different outlook, though, Stepashin urged the Clinton administration to help 10 million people in Serbia, Yugoslavia's dominant republic, who face winter with insufficient fuel and water.
Right now, in the summer, they are getting by, Stepashin said. "But there will be catastrophe in the winter in the heart of Europe," he warned.
The prime minister said he told Clinton in their half-hour meeting that "joint work" was need to alleviate the hardships.
On Monday, Berger repeated U.S. policy that not one cent in U.S. aid will go to the reconstruction of Serbia so long as Yugoslav President Slobodan Milosevic remains in power.
Berger did not exclude humanitarian assistance but said Russia was primed to provide it. Stepashin said Moscow indeed would contribute $150 million to help the Serbs.
An international donors conference was scheduled for Brussels, Belgium, on Wednesday, and Clinton and other world leaders are meeting Friday in Sarajevo, Bosnia, to discuss stabilizing the Balkans.
Stepashin made his pitch for the Serbs in a friendly way. He said relations with the United States have turned a corner, and he thought an agreement could be worked out.
"If you are trying to find a problem in our relationship, you can find it," he said during a speech at the National Press Club. "But let's get away froit."
Trolling for American capital and good will, Stepashin offered assurance that Russia's rocky economy is on the upswing. He said American investors "can come without fear of racketeers."