Secretary of State James A. Baker III met with Jordan's King Hussein Tuesday and said afterward that all parties he has consulted with in his Middle East diplomacy "have agreed essentially" to attend a regional peace conference.

But Baker acknowledged that "the possibility of a U.N. role" was still a sticking point in the way of convening such a meeting.He met with reporters after more than three hours of talks with Hussein, who told reporters at a news conference: "I believe we share a total commitment to the cause of peace in this region that is long overdue."

Hussein added, "I believe this chance that now exists for a peace process to start . . . will probably never come again," although he dodged questions about his own country's participation.

Baker is on his fourth trip to the Middle East since the end of the Persian Gulf war. He drove to Israel from Jordan after meeting with the king.

"It's my understanding that all of the parties with whom we have had discussions have agreed essentially to attend a conference sponsored by the United States and the Soviet Union for direct negotiations between Israel and the states neighboring Israel and for direct negotiations between Israel and Palestinians," Baker told reporters at the news conference.

His caution that there remained differences over a U.N. role came on top of comments on Monday, when he outlined several obstacles, including the role of the U.N. and the question of Palestinian representation.

Baker walked across a Jordan River bridge on his way to Jerusalem, saying he wanted to get a feel for the geography of the Middle East conflict.

The secretary of state chose a novel route to Israel on his latest Middle East peace shuttle, traveling by car from Amman, Jordan, through the Israeli-occupied West Bank to Jerusalem. "I wanted to get a sense of the distances involved here and I have," Baker said.

Baker conducted his diplomacy as President Bush said he was not discouraged about prospects for a Middle East peace conference despite the remaining differences. "There's room for optimism," he contended.

Despite Hussein's comments about the desirability of peace, the Jordanian monarch would not say if he would attend an international Mideast peace conference if Syria refused to participate.

Syria is insisting on a United Nations role in such a conference, but Israel has rejected that idea.

Syria also wants assurances that a Mideast peace conference would meet regularly to check progress. Israeli leaders want to adjourn immediately into bilateral talks following a one-time international gathering.

When asked whether he would refuse to attend a peace conference if Syria was not represented, Hussein replied, "I haven't said that."