MOSCOW — With relations between Russia and the United States on edge over Syrian policy and strident anti-American statements by the Russian government in response to political protests here, the Obama administration and its Democratic allies in Congress have begun an aggressive push to end cold-war-era trade restrictions and make Russia a full trade partner.

The seemingly incongruous and politically fraught campaign to persuade Congress to grant permanent, normal trade status reflects a stark flip in circumstances: suddenly, after more than 35 years of tussling over trade, Russia has the upper hand.

In December, Russia became the last major economy to win admission to the World Trade Organization — a bid that was supported by the Obama administration because it required Russia to bring numerous laws into conformity with international standards, including tighter safeguards for intellectual property. It was also part of the so-called reset in relations with the Kremlin.

But if Congress does not repeal the restrictions, adopted in 1974 to pressure the Soviet Union to allow Jewish emigration and now largely irrelevant, the United States will soon be in violation of W.T.O. rules. American corporations could be put at a serious disadvantage — paying higher tariffs, for instance, than European and Asian competitors, which would immediately enjoy the benefits of Russia’s new status.