President Reagan sought to shore up his support among wavering urban ethnic groups today by reminding them of their shared desires for anti-abortion legislation, a constitutional amendment supporting school prayer and tuition tax breaks for families with children in parochial schools.

In his speech here to the centennial convention of the Supreme Council of the Knights of Columbus, Reagan in effect was preaching to the choir.

Cheers and applause from cardinals and other clergy on the platform behind him and the convention delegates who filled the Hartford Civic Center frequently interrupted his rambling litany of their common aims, which also included crime-control legislation, a strong nuclear deterrent and what Reagan described as "the belief in the importance of the family, community and church."

"Now, perhaps some of you remember that, just a few years ago, these basic values were being forgotten in the highest levels of our government--indeed, the machinery of government at times actively opposed them," he said.

"Government intrusion into the life of the family and the local neighborhood--federally financed abortions, forced busing, HEW regulations and rules on many matters that government had no business dealing with--had reached unparalleled heights."

Reagan traveled here by Air Force One this afternoon from Iowa, where he spoke yesterday to corn farmers in a similar effort to rebuild support among constituencies that helped elect him but are now growing wary as the country remains stuck in recession.

As he had with the farmers, Reagan told the Knights of Columbus that his policies would bring about economic recovery. He blamed the nation's problems on his Democratic predecessors and years of Democratic policies of too much taxing and government spending.

Reagan's two-day whistle-stop trips to the hustings are experimental efforts by aides on how to best use him in the fall congressional election campaigns. They believe that if he is to be of value to GOP candidates he must rebuild support he has lost since taking office.

It is a deliberate strategy of keeping him above the battle. The aim is to make him appear more presidential and concerned about issues. He has assiduously avoided hard stumping for political candidates on this trip. And he has held no fund-raisers.

But, as a demonstration of the White House's eagerness to minimize GOP losses and keep control of the Senate, Sen. Lowell P. Weicker (R-Conn.), Reagan's most outspoken GOP critic in the Senate, was invited to ride back to Washington on Air Force One with the president.

Asked about the speech, Weicker replied, "Obviously, I disagreed with the entire substance of it."

Asked why he rode the plane, he responded, "It's a convenient way back."

Reagan's speech here lauded the Knights of Columbus for their "stalwart faith in religious and family values," their community service and charitable contributions.

While Reagan forcefully declared his belief in "human life legislation," he declined to referee the dispute among anti-abortion groups over which of three bills pending in the Senate should pass. He simply noted the sponsors of the three bills and urged "the speedy consideration they deserve."

Both here and in Iowa, his aides paid meticulous attention to the visual impression of his efforts, a concern overseen by his deputy chief of staff, Michael K. Deaver.

The special visual event here today was a working luncheon with Cardinal Agostino Casaroli, Vatican secretary of state and the personal representative of Pope John Paul II to the convention.

After the luncheon, White House deputy press secretary Larry Speakes said Reagan and the cardinal discussed their "mutually reinforcing" policy positions in Poland and Lebanon.

Yesterday, the photo opportunity was a visit to an Iowa hog farm where a shirtsleeved Reagan ate home-made ice cream and discussed agricultural issues with a selected group of farmers. The White House advance team had set up a sound system so that reporters could hear the exchange, but on orders of Deaver it was dismantled shortly before Reagan's helicopter arrived.

Asked why, Deaver told reporters the farm visit was a "picture story."

When he spoke to the National Corn Growers Association in Des Moines yesterday, Reagan, promising that they would be able to sell a "record volume" of grain to the Soviet Union, remarked on how martial law had eased somewhat in Poland.

But to the Knights of Columbus, he returned to his familiar hardline anti-Soviet rhetoric, recalling with special relish the hostile reaction of the Russians to his sharp denunciation of them in a speech to eastern European ethnic groups in the White House Rose Garden last month.

Reagan's political strategists are gambling that he can ride out the current economic storm, because the polls indicate that most people seem to agree with him that the Democrats are to blame and that it will take time to straighten the problems out.

But the polls also indicate an ambivalence on the part of the public. Reagan's own pollster, Richard Wirthlin, said that when he asked whether Reagan's economic program would ultimately help or hurt the economy, only a "mild majority" said they believed it would help.

A Washington Post/ABC News survey found that a majority believed Reagan's program would eventually work, but when asked a larger majority said he should drop his program and try a new one.