Senate Majority Leader Robert C. Byrd (D-W.Va.) said yesterday he has received assurances from Soviet leaders that they will stay quiet while the Senate debates the SALT II treaty, even if American rhetoric becomes "hot-header."

Byrd added that the Soviet chiefs "raised no objections whatsoever" when he outlined a number of reservations and understandings he thought the Senate was likely to add to documents other than the treaty text.

Resuming his regular Saturday morning press conferences following a one-week trip to the Soviet Union, Byrd also said he opposes any "massive tax cut" proposal at this time. He said President Carter was "wise" to have postponed his energy speech as long as he did, and added that Congress is ready for action on the energy crisis.

Byrd said he would make his own decision on the arms limitation treaty sometime around the Senate's August recess. If he wished to indicate a favorable decision, he said, he would oppose any amendments to the text.

Soviet leaders ruffled senatorial feathers last month by declaring bluntly that any amendments would scuttle the pact. Byrd said he took pains to distinguish in his talks with them between the pact itself and a separate resolution of ratification that could contain additional understandings and reservations.

In discussing the pact with Soviet Foreign Minister Andrei Gromyko for 2 1/2 hours, Byrd said, "I told him that just because a senator makes a strong statement today doesn't mean he'll vote against the treaty tomorrow."

Gromyko, Byrd said, responded that "If he heard a hotheaded - and he said hotheaded - statement from our side and his right hand was about to write a response, his left hand would reach over and pull it back."

Further, Byrd related, Gromyko promised to "make sure his dictaphone was broken and tell his secretary she wasn't well and to go home."

Soviet President Leonid I. Brezhnev appeared "#attentive, alert" during the hour and 45 minutes Byrd spent with him. Neither Brezhnev nor Gromyko made any response when Byrd outlined the conditions he thought the Senate would be likely to impose, "but they conceded that our deliberations would be fair and careful," Byrd reported.

Those conditions, he said, might include understandings to build no more than 30 Backfire bombers in any one year, as Brezhnev has promised; not to extend the treaty past 1981 without the consent of two-thirds of the Senate, and not to circumscribe U.S. collaborations with European allies.

Acknowledging that amendments to the text proposed by Minority Leader Howard H. Baker Jr. (Tenn.) could prove fatal to the treaty, Byrd said, "I don't think Sen. Baker has closed the door" on the pact's future yet.

Turning to domestic matters, Byrd said he opposes a $36 billion tax cut outlined Friday by House Republicans. "It would just ignite expolosive inflation," he said.

Byrd commended President Carter for seeking a variety of views on the energy situation but said that Congress had not waited for presidential decrees before acting. "The train is halfway past the station already," with various bills pending in both houses, Byrd said.