House and Senate conferees broke a seven-week stalemate yesterday and agreed on a $4 billion local public works bill that is a key part of President Carter's economic stimulus package.

After eight meetings, the conferees agreed to set aside for now a fight over unrelated water pollution policy in order to get the public works program into action during this construction season. It is expected to create about 160,000 jobs.

Carter sent word that he was "highly pleased" that one piece of the stimulus package he sent Congress three months ago is on the verge of final passage. It must be approved by both houses before going to Carter for his signature.

The public works program was a congressional initiative, first enacted into law over President Ford's veto last year at a $2 billion level. Congressional leaders persuaded Carter to ask Congress for another $4 billion this year.

The House quickly approved the public works money in February. But when the Senate took it up on March 10 it added $9 billion to build sewage treatment plants for a separate program of water pollution abatement.

The House, which has tried for two years to make several substantive changes in the water pollution program to speed improvements of the nation's streams, refused to approve the $9 billion unless the Senate agreed too several long-range policy changes.

During a series of meetings before and after the Easter recess, House and Senate conferees seemed to be moving closer.

But yesterday afternoon the Senate conferees suddenly announced that they weren't going to give any more and that the House could either accept their latest offer or drop the entire water fight and let the public works bill go free. The House conferees, who had proposed doing that three weeks ago, agreed.

Edmund S. Muskie (D-Maine), chairman of the Senate's clean water subcommittee and principal opponent of some of the House amendments, said he proposed dropping the water fight - despite an immediate need for the money - in order to get the public works program going this year. Jennings Randolph (D-W.Va.), chairman of the Senate Environment and Public Works Committee, said that "after three months the American people have a right" to see a jobs bill move to the President's desk.

The conferees had settled minor differences on the public works program last week. The bill authorizes $4 billion to be allocated among the states under the formula in the Senate bill. This distributes 65 per cent to states on the basis of the highest numbers of unemployed and 35 per cent to areas of more than 6.5 per cent unemployment regardless of size.

The congress also approved an amendment adopted by the Senate during the angry debate with the President over his plans to delete funds for various water resource projects from next year's budget. The amendment orders the administration not to cut back spending on these projects in the remaining months of this fiscal year.

Because of the two-year House-Senate fight over water pollution policy, the program was not funded for the fiscal year that began Oct. 1 and states are beginning to run out of money. Congress has just provided $1 billion for this year in a supplemental appropriations bill, but that is far less than can be used.

The battle over water pollution policy probably will be joined again later this year.