After months of bickering, a bipartisan group of Senate Judiciary Committee members yesterday agreed on a compromise that would dramatically strengthen the 1965 Voting Rights Act and virtually assure quick agreement this year on an extension. President Reagan immediately announced that he would endorse the compromise.

"Voting is one of the most cherished of our birthrights as American citizens. When practiced, it enriches our democracy. When threatened, it must be protected," Reagan said. "Today, I not only want to salute the efforts of those who have forged this compromise, but I also want to give it my heartfelt support. My hope is that it will now pave the way toward swift extension of the Voting Rights Act by the entire Congress."

The compromise is supported by civil rights groups, including the NAACP and the Leadership Conference on Civil Rights, and by about 70 senators, ranging from liberal Democrats to conservative Republicans. Reagan's support was expected to draw hard-line senators onto the list of supporters.

The agreement, worked out by Sens. Robert J. Dole (R-Kan.), Edward M. Kennedy (D-Mass.) and Charles McC. Mathias (R-Md.), would prohibit state and local officials all over the country from using any voting practice or procedure that results in discrimination against blacks and other minorities.

That standard is considerably easier to prove than the one in effect since a 1980 decision by the U.S. Supreme Court: that the law is violated only when state or local officials consciously intended to discriminate.

There was general agreement that the act needed to be extended. But the administration up until yesterday had argued against the results standard on the grounds that it could lead to lawsuits calling for proportional representation by race in municipalities all over the country.

Last October, the House voted, 389 to 24, for a bill which also included the easier-to-prove results standard. That bill contained specific language providing that proportional representation could not be required.

The Dole-Kennedy-Mathias compromise goes beyond the House language and makes it clearer that there will be no requirement that minority groups like blacks or Hispanics be elected in proportion to their numbers in the population. Instead, it defines the issue as whether those population groups have equal access to the political process.

Reagan said yesterday he was satisfied "the compromise would greatly strengthen the safeguards against proportional representation while also protecting the basic right to vote."

Benjamin L. Hooks, executive director of the NAACP and chairman of the Leadership Conference, called the compromise "a good, fair and effective extension measure."

Dole said that when the Judiciary Committee meets today to consider the bill, he expects to have the support of at least 13 of the 18 members.

Chairman Strom Thurmond (R-S.C.) has not yet said whether he will support the compromise, but staff members said that is a possibility. After efforts last week by conservatives like Sen. Jesse Helms (R-N.C.) to use procedural methods to slow down committee action on the issue, Thurmond promised to hold night sessions of the committee this week if that is necessary to move the bill through.

Both Kennedy and Dole warned that floor action on the bill must be completed this month in order to avoid a conflict with upcoming action on the budget and the debt ceiling. Sections of the act are scheduled to expire in August.

Congressional sources said they believed the House would easily approve the changes in the compromise.

The compromise bill goes beyond the House-passed bill in defining discriminatory results. It says a court should look at a "totality of circumstances" in a community to determine if the "political processes leading to nomination or election . . . are not equally open to participation" by minorities.

It provides that the number of minorities elected in the past is just one factor to be considered in determining whether a violation has occurred.

The compromise would extend for 25 years the requirement for certain jurisdictions with a history of voting discrimination to preclear changes in election laws with the Justice Department. After the first 15 years, Congress would review the "bailout" criteria by which those jurisdictions could be exempted from the preclearance requirement after a period of good behavior.

The House bill used the same bailout criteria, but had no time limitations.