President Carter's appeal for an end to violence in Northern Ireland received a generally cool reception today in Ireland and Britain.

The official response in both Dublin and London was favorable. But elsewhere, the comments issued by the White House yesterday were regarded as largely platitudinous.

"They will have no practical consequences, I think," said Conor Cruise O'Brien, a noted historian of the Ulster struggle and a senator in the Republic of Ireland. "It's all rather tired."

British papers were more caustic. The Daily Mail termed Carter's statement "a very damp squib." The Manchester Guardian said he had "confined himself to a general condemnation of sin in Northern Ireland and an even more generalized endorsement of virtue." The Daily Telegraph termed the statement "a curiously Olympian pronouncement."

In his statement, the President said he would support any solution backed by the Catholic and Protestant communities - and promised to encourage American investments in Ulster when peace comes.

Dublin papers were almost as blunt as the British. The Irish Times said the President's "entry on the scene . . . has been modest enough." Its editor, Douglas Gageby, said Carter had given "a bit of help to comfort beleaguered Taigs [Catholics] in the North, but I don't think it's worth a damn bit more." The Irish press called it "little more than the predictable list of platitudes."

British Prime Minister James Callaghan also welcomed Carter's remarks. It is believed here that British officials persuaded Carter to abandon his earlier intention to come out strongly for "power-sharing" between Catholics and Protestants. London is still formally committed to such a solution but in deference to Protestant sentiment, has been edging away from it.

In Northern Ireland, William Craig, a leading Protestant politician, said, "There is really nothing in the statement to get worked up about."