In this story:

• Clinton wins concessions from both sides
• King Hussein helps with 'tough choices for peace'
• Related stories and sites

WYE MILLS, Maryland (CNN) -- A comprehensive deal was close to being finalized early Wednesday at the Mideast peace summit, Israeli and Palestinian sources told CNN. The deal was to be finished Wednesday, with a signing ceremony expected to take place at the White House on Thursday, Israeli sources said.

State Department spokesman James Rubin said Tuesday afternoon that the talks had reached the "endgame" stage.

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"We're into a phase of very hard bargaining. A lot of the underbrush has been cleared away," Rubin said. "Some obstacles have been overcome, but significant gaps remain."

Jordan's King Hussein, who has good relations with both Palestinian leader Yasser Arafat and Israeli Prime Minister Benjamin Netanyahu, raised the optimism when he joined the talks Tuesday.

Clinton wins concessions from both sides

President Clinton, who has spent most of the last six days involved in the talks, apparently won concessions from both sides Monday. Clinton remains at the talks to try and work out the final details.

Clinton is said to have won an agreement from Netanyahu to give up 13 percent more territory on the West Bank to the Palestinians. In addition, the Israelis would relinquish another 14.2 percent of the West Bank that it now shares with the Palestinians.

Arafat has agreed to revoke the Palestinian charter with its anti-Israeli provisions, sources said. The Palestinians have also agreed to arrest 30 fugitives that Israel wants imprisoned.

In addition, both sides have agreed to a complex and comprehensive security package.

They have also apparently agreed to delay consideration of a third-phase redeployment of Israeli troops, leaving that issue to U.S. envoy Dennis Ross to mediate later.

Finally, Palestinian sources said the issues of safe passage, a Gaza airport, the release of Palestinian prisoners, economic aid and a seaport in Gaza remained under discussion.

King Hussein helps with 'tough choices for peace'

Hussein, who has been in the United States for cancer treatment, is viewed by both sides as a peacemaker. Jordan signed a peace treaty with Israel in 1994, and because of the large number of Palestinians among his subjects, Hussein had pushed continually for a peace settlement on the West Bank and Gaza.

Rubin said the United States believes "the King will help bring home the importance of making tough choices for peace."

Clinton canceled a campaign fund-raising trip to California Tuesday to return to the peace talks.

"Given the importance of the issues at hand, the president and Prime Minister Netanyahu and Chairman Arafat believe it is appropriate to stay and work on these important issues," said White House spokesman Joe Lockhart.

The United States invited the two sides to come to Maryland last week to consider a package of proposals that the United States hopes will move the talks forward and allow for the beginning of final status talks between Israel and the Palestinians.

The talks are a crucial juncture in the long-stalled Mideast peace process because the parties face a May 4, 1999, deadline. If no West Bank deal emerges by then, Arafat has said he will unilaterally declare a Palestinian state -- a move of potentially explosive consequences for the region.

State Department Correspondent Andrea Koppel contributed to this report.