The Senate overwhelmingly rejected Friday an attempt by conservative critics of the U.S.-Soviet missile treaty to link the pact to alleged Soviet cheating on five other arms-control agreements.

In a series of five votes, the Senate killed, piece by piece, the amendment proposed by Steve Symms, R-Idaho.Symms' amendment noted that Reagan has told Congress the Soviets are violating the SALT I and SALT II arms-limitation treaties, a 1963 pact banning open-air atomic tests, a 1925 Geneva protocol banning chemical weapons and the 1972 Anti-Ballistic Missile treaty.

His proposal would have required that the administration certify the Soviets are in compliance with all these pacts before the Intermediate-range Nuclear Forces (INF) treaty could have taken effect.

Conservatives, using Senate rules, insisted on five separate votes rather than a single roll call. In the tallies, the votes to kill Symms' proposal were 85-11, 87-10, 86-11, 82-15 and 89-8.

The decision came after Senate Republican leader Bob Dole of Kansas called on his fellow Republicans to speed up the action.

"We need to start making real progress on the treaty itself," Dole said. "Time is of the essence; the president leaves next Wednesday" for his Moscow summit with Soviet leader Mikhail S. Gorbachev.

Dole said Republican senators have "a special burden" to assure that Reagan does not go to Moscow without ratification of the INF treaty.

Sen. Ted Stevens, R-Alaska, a member of the Senate observer term that monitored the INF talks, told the Senate, "As one of them, I can stand before the Senate and say I have confidence in this treaty; it need not be changed at all."

Symms said his amendments "simply mean that the treaty does not go into effect until the president can report the Soviets are in compliance with existing arms treaties."

Sen. David Durenberger, R-Minn., opposed the Symms proposal because he said "it is designed to kill the INF treaty, not to produce Soviet compliance."

Sen. James J. Exon, D-Neb., complaining of Republican stalling, referred to Symms' proposal as "nonsense and extraneous."

"I think this is a terrible situation," Exon said. "It would cripple the president as he represents the United States and the free world." "

Exon said Reagan will be partly to blame if the treaty isn't approved before the summit. "The president could put his foot down. He is the president. He is the leader of the Republican Party without question. I think he is contributing to his own problems."

As debate on the amendments opened Thursday, Symms told the Senate: "The Soviets cheated in the past and I think we can expect they're going to cheat in the future."

But Sen. Claiborne Pell, D-R.I., chairman of the Foreign Relations Committee, noted that the Reagan administration says this treaty should be considered on its own merits.

"To my mind, the important thing is what does this treaty do; does it help our security or harm it?" Pell asked. "I don't think we ought to be in the position of cutting off our nose to spite our face."