President Reagan has offered his full support for a major revision of the nation's immigration laws, clearing the way for action in the House, Rep. Peter W. Rodino Jr. (D-N.J.) said yesterday.

"The president assured me that he was . . . deeply interested in comprehensive immigration reform. When I told him that . . . it would take his personal involvement and leadership, he assured me he would do everything," said Rodino, the House Judiciary Committee chairman, after a meeting at the White House.

Rodino said James C. Miller III, the director of the Office of Management and Budget, told the group that the legislation's estimated cost of $1 billion a year over the next four years "was fine." The White House declined to comment on the meeting.

Sen. Alan K. Simpson (R-Wyo.), who has led Senate efforts for immigration change, said through a spokesman that he was "very pleased" with the meeting and "optimistic" that Congress may enact a bill this year. He said the meeting did not include a discussion of "specifics."

The Senate approved an immigration bill last year that provided criminal and civil penalties for employers who hire illegal aliens, an amnesty program for undocumented aliens who have been in the United States for a fixed number of years and increased funding for enforcement of U.S. immigration laws.

Estimates of the number of illegal aliens in the United States run as high as 6 million.

Attorney General Edwin Meese III, who also attended yesterday's meeting, has said that the administration, in general, favors comprehensive changes in immigration law.

Rodino, who said he was waiting for a commitment from the president before bringing the issue before the Judiciary Committee, had stressed earlier that he would not be willing to push the controversial legislation, especially in an election year, unless he had bipartisan support and the backing of the White House.

Legislation dealing with changes in immigration law has been repeatedly opposed by groups led by Hispanic Americans and U.S. growers who depend on foreign migrant labor. Hispanic leaders and civil liberties groups have opposed the current House and Senate proposals, charging that they will encourage job discrimination against Hispanic Americans and legal Hispanic immigrants.

The chances for congressional passage improved last summer when Rodino introduced his version of the immigration bill. He had not sponsored such legislation since 1975, when his last effort died in the House Rules Committee.

Simpson has said he expects major changes as the bill moves through Congress and that he is willing to compromise as long as it contains the employer sanctions, an amnesty program and increased funding for enforcement