AGAIN, VIOLENCE intrudes upon peacemaking in the Middle East. A mainstream PLO group claimed responsibility for murdering three Israelis in Cyprus, and, citing that deed, Israel yesterday conducted air attacks on PLO headquarters in distant Tunis. The preliminary American judgment was, unexceptionably, that the air strike was a legitimate act of self-defense. But the strike is also bound to burden even more an effort at reaching peace that was already having difficulty getting under way.

The Cyprus killings had made it marginally harder for Israel to stay the diplomatic course. The Tunis attack may weaken Yasser Arafat's work-with-Jordan wing of the PLO and leave King Hussein -- embarrassed even as he visited Washington -- without the Palestinian partner he needs to step ahead. This would hurt. King Hussein, dragging part of the PLO uncertainly behind him, has just endorsed "prompt and direct" negotiations with Israel. These previously unspoken words were taken in some quarters merely as an exercise he had to go through to help the Reagan administration best the Israel lobby's opposition to a new American arms deal with Jordan. But, in the Middle East, such words are important; people may live and die by them.

Despite the violence, the Jordanian arms package remains on the congressional agenda. Advocates of the deal have to press the Israelis and their congressional allies to grasp the strong American interest in the political health of King Hussein. They must press the king to keep refining his terms. With a hostile Syria breathing down its neck, Jordan has a good military case for needing a new arms pipeline and a good political case for needing the visible mantle of American patronage.

When the king offered "prompt and direct" negotiations, the prime minister of Israel saluted his "vision of peace" and the opposition deputy prime minister dismissed his "verbiage." They joined in rejecting the Hussein demands that negotiations 1) take place in a U.N. forum including Moscow and 2) cover the PLO. But Israel should not want to leave an impression that, while the king is moving, it is digging in. On the new arms package, Jerusalem worries lest a rearmed Jordan join another Arab war against Israel. Jerusalem might better worry that a Jordan frustrated in Washington may turn to another supplier, as Saudi Arabia has just turned to Britain, for arms on which there are no American controls.

Here a firm American attitude is essential. But the administration's effort to compose a Jordanian- Palestinian delegation to negotiate with Israel is wobbling. No political decision is yet evident to invest the high-level prestige and energy necessary to advance a peace initiative and to cope with the regional turbulence it will surely generate. The administration's notion of linking arms deals and peace moves is sound, but the process has to be handled with care and -- as the latest violence shows -- with all deliberate speed.