Regardless, some experts said it could help relations by eliminating what the Russians had cited as one of their main objections — the interceptors in the final phase of the missile shield that might have the ability to target long-range intercontinental ballistic missiles, which are part of Russian’s nuclear arsenal.

The Obama administration has sought cooperation from Russia on numerous issues, with varying degrees of success. Russia generally has supported the NATO-led military effort in Afghanistan and has helped to restrict Iran’s nuclear program by supporting economic sanctions. But the two countries have been deeply at odds over the war in Syria, and over human rights issues in Russia. Most recently, Mr. Obama has said he would like further reductions in the two countries’ nuclear arsenals, something Russia has said it would not consider without settling the dispute over missile defense.

American experts insisted that the Russians’ concern over the antimissile program was exaggerated and that the system would not have jeopardized their strategic missiles had the final phase been developed. That Russian concern has now been addressed.

“There is no threat to Russian missiles now,” said Steven Pifer, an arms control expert who has managed Russia policy from top positions at the State Department and the National Security Council. “If you listen to what the Russians have been saying for the last two years, this has been the biggest obstacle to things like cooperation with NATO.”

“Potentially this is very big,” said Mr. Pifer, now of the Brookings Institution. “And it’s going to be very interesting seeing how the Russians react once they digest it.”

In Washington, many officials have said they believe Russia’s real objections are not only about the particular capabilities of the missile shield but also about a more general political and strategic opposition to an expanding American military presence in Eastern Europe. Canceling only the final stage of the program does not address that concern, so it is possible that Russia’s position will remain unchanged.

Sean Kay, a professor at Ohio Wesleyan University and expert in international security issue and Russian relations, said that the so-called fourth stage of the Europe-based missile defense program “was largely conceptual” and might never have been completed.