DETERMINED to keep the fledgling Middle East peace process alive, the Bush administration has again seized the initiative by issuing invitations to Israel and its Arab neighbors to attend face-to-face talks Washington.Three weeks ago the United States and the Soviet Union put the squeeze on reluctant Israeli and Arab leaders to attend, in Madrid, the opening phase of the first Middle East peace conference in over a decade. The event was largely ceremonial, but historic, since it was the first time Arab states other than Egypt had agreed to meet with Israel. Barring an unlikely snag, the second phase of the peace process will begin in Washington on Dec. 4 when Israel enters into separate, direct negotiations with Syria, Lebanon, and a joint Jordanian-Palestinian delegation. Phase 3 of the peace process - regionwide talks on water, arms control, and economic development - is also planned, but no date or venue has been set. The administration decided to send invitations to meet in Washington after protracted wrangling over where to hold direct talks threatened to disrupt the fragile momentum generated in Madrid. At this writing only Jordan had formally accepted the invitation, but a Palestine Liberation Organization spokesman, Bassam Abu-Sharif, was quoted by Radio Jordan as saying the Palestinians had decided to accept. US officials believe all the parties will be under considerable pressure to accept. Syria cannot afford to be left out of the peace process, which offers the only hope of regaining the Golan Heights from Israel. Palestinians need to attend because peace talks offer the last chance to gain eventu al control over at least part of the Israeli-occupied West Bank and Gaza Strip. If Israel says no, it jeopardizes a longstanding request for $10 billion in US loan guarantees needed to help settle a flood of new Soviet immigrants. None of the parties will want to be blamed for the collapse of the first serious peace talks in years. In Madrid, conversations between Israelis and Palestinians got off to the most promising start. During the second round the two sides are expected to make progress on defining terms for temporary self-government for West Bank and Gaza Palestinians. But defining the final status of the territories will be difficult because Israel refuses to give up sovereignty, while Palestinians demand an independent state.