Four American Roman Catholic bishops, after touring Northern Ireland, said today the British government must be the "important actor" in finding a political solution to end the "desperation" of pervasive unemployment, job discrimination and violence there.

While calling it "reprehensible" for Irish Americans to give money knowingly to support violence, Archbishop John J. O'Connor of New York warned that the problems of British-ruled Northern Ireland go well beyond trying to end the violence of the Provisional Irish Republican Army and other Catholic and Protestant terrorist groups.

Appearing with the three other U.S. bishops at a press conference here after four days in Ulster, O'Connor said people must "look more carefully" beyond the IRA volence "at what are alleged to be the underlying causes, the injustices, that provoke violence."

Bishop James Malone, president of the National Conference of Catholic Bishops, spoke of the "evident job discrimination" and unemployment rates running to "40, 50 and even 60 percent among Catholics," who make up about one-third of Ulster's population.

The bishops also visited prisons in the North and families of prisoners. Without commenting on the innocence or guilt of those jailed, who are mostly Catholic, they said in a joint statement that "we are greatly concerned about the allegations of indefinite imprisonments without trials, charges of abuse in strip-searching, and the widespread distrust among certain communities of the judicial system in general."

Bishop Mark Hurley of Santa Rosa, Calif., said there are poor Protestants who also "feel as trapped as many Catholics" and that the biggest point stressed to the visiting bishops was the need for Americans to understand "the key role Britain has to play in solving the problem."

"The ball is in the court of the British government," Hurley said, particularly since publication in May of a report by the New Ireland Forum, composed of the main moderate Roman Catholic parties of Northern Ireland and the Irish Republic, that called for a "major reassessment" of British policy on Ulster.

"All segments of the population here are almost in desperation looking to see what will happen, to see if the British government will open the door for progress," he said.

Hurley said that "without apologizing for the IRA," which has waged a 15-year campaign of violence against British rule, Americans' "tendency to make the IRA the only issue is a serious mistake."

Malone said the bishops' visit has led them to a new understanding that the root cause of Ulster's violence and unemployment was the need for a political solution there, and that "an important actor in this must be the British government."

The bishops spoke here a few weeks before British Prime Minister Margaret Thatcher is due to come to Dublin to discuss Northern Ireland with Irish Prime Minister Garret FitzGerald, the main force behind the New Ireland Forum report.

The Irish are pressing for Britain to make some positive new initiative that would keep the spirit of reconciliation going. But Thatcher said publicly last week that she does not see any new initiative Britain could make and that peace can only come if Northern Ireland's divided factions decide they want it.