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WYE MILLS, Maryland (CNN) -- Middle East mediation efforts were stepped up on Tuesday as King Hussein of Jordan was expected to join the current Israeli-Palestinian summit in this secluded U.S. location.

"We believe he can play a constructive role in the (peace) process," White House spokesman Joe Lockhart told reporters at a briefing.

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King Hussein is currently in the United States for cancer treatment. His country has a peace treaty with Israel, and he is viewed by both Israelis and Palestinians as a peacemaker. Not least because of the large number of Palestinians among his subjects, Hussein has pushed continually for a peace settlement in the West Bank and Gaza.

There was no official word from the Wye conference on whether Israeli Prime Minister Benjamin Netanyahu and Palestinian Authority President Yasser Arafat had moved any closer to an agreement on how to proceed with Palestinian autonomy in the West Bank.

"There are significant gaps between the parties," Lockhart commented, adding that U.S. President Bill Clinton was determined to help the two parties take the "hard decisions necessary to move the peace process forward."

Clinton was to rejoin the talks early Tuesday afternoon.

The president was said to have won an agreement from Netanyahu to give up 13 percent more territory in the West Bank.

In addition, the Israelis would turn over to Palestinian control another 14.2 percent of the West Bank that is now shared with the Palestinians.

Arafat, sources said, had agreed to revoke the Palestinian charter with its anti-Israeli provisions. And the Palestinians reportedly also agreed to Israeli requests that they arrest 30 fugitives.

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

Both sides apparently agreed to delay consideration of a third-phase redeployment of Israeli troops, leaving that to U.S. Middle East envoy Dennis Ross for mediation at a later stage.

Arafat has been pressing for a complete agreement. Netanyahu, sources said, also favored such an agreement if Arafat would "do his part."

Correspondent Andrea Koppel contributed to this report.