The Senate yesterday agreed to begin debate on the controversial natural gas price decontrol bill on Monday, with a key vote to recommit the bill to conference likely sometime later in the week.

Senate Majority Leader Robert C. Byrd (D-W.Va.) could not persuade opponents of the legislation to accept a fixed time for a vote, so there is still a possibility of a filibuster or other parliamentary delaying tactics.

President Carter is leading an all-out administration effort to win passage of the gas bill, which Carter has called a crucial test of the nation's will.

The legislation is opposed by an unusual coalition of liberal Democrats who oppose price decontrol, Republicans who oppose Carter's general policies and oil-state conservatives who regard the complex gas bill as worse for the gas industry than no bill at all.

Both proponents and opponents had some heartening news yesterday.

Proponents were encouraged by an endorsement of the bill by Sen. Edmund S. Muskie (D-Maine), the influential chairman of the Senate Budget Committee, who had opposed total deregulation of newly-discovered natural gas prices the last time the Senate voted on the issue.

Aides to Muskie said he was swayed by arguments that the international repercussions of defeating the bill could be serious, and by an analysis produced in the Congressional Budget Office concluding that the bill would neither contribute unduly to inflation nor unfarily gouge homeowners who use gas.

Administration officials, said the CBO report should help them. They were also pleased by a new analysis of the gas bill produced by the Federal Energy Regulatory Commission (FERC), which will have to administer the complex legislation if it passes.

Last month the director of FERC's enforcement office, Shelia S. Hollies, produced a memo on the original version of the compromise, saying it would be too complicated to administer. This memo was quickly leaked to the press.

That memo led to substantive alterations of the conference report, and yesterday the commission released its commentary on the revised version. FERC Chairman Charles B. Curtis said yesterday in a letter to Sen. Henry M. Jackson (D-Wash.), chairman of the Senate Energy Committee, that the new version "can be effectively administered and enforced."

Opponents of the bill had already made good use of the earlier FERC memo assailing the bill's complexities and ambiguities, so now proponents can respond with this new memo.

However, as Curtis pointed out in his letter, the bill still creates a "most difficult" challenge for FERC, and can only be enforced if Congress appropriates finds for new regulatory personnel. Moreover, Curtis noted, it may take years of litigation to establish what the new bill really means.

Opponents of the gas bill were encouraged yesterday by indications that Sen. Russell B. Long (D-La.), the ingencious chairman of the Senate Finance Committee, will be working hard to beat the bill. Long and Sen. Clifford Hansen (R-Wyo.) joined in sending a mailgram assailing the bill yesterday to 110 chief executives of major corporations.

The two said that relating the fate of the legislation to the future of the dollar was "poor economics and poor logic." "It does not honor to our national will to adopt a bad bill," they said.

Sen. Howard H. Baker Jr. (R-Tenn.), the minority leader, publicly affirmed that he, too, will oppose the bill, though it remains to be seen how hard Baker will work to block it. Sources on both sides regard his role as potentially crucial.