AMMAN, Jordan (AP) — U.S. Secretary of State John Kerry on Saturday renewed his push to ease violence and tension between Israel and the Palestinians in talks with Palestinian President Mahmoud Abbas and Jordan's King Abdullah II.

Meeting in Amman, Kerry, Abbas and the king were exploring ideas, first raised during a Thursday meeting in Berlin between Kerry and Israeli Prime Minister Benjamin Netanyahu, on how to defuse the situation. Over the past five weeks, 10 Israelis have been killed in Palestinian attacks and 49 Palestinians killed by Israeli fire, including 27 said by Israel to be attackers.

Both Kerry and Abbas expressed hope that a solution could be found in brief comments to reporters as they began their meeting.

"All the time we had the hope," Abbas said. "We did not lose the hope."

Kerry added: "I am hopeful."

After seeing Abbas, Kerry met the Jordanian monarch. Neither spoke to reporters as they began their talks.

Following his meeting with Netanyahu in Germany, Kerry said he was cautiously optimistic about calming the situation. Kerry has said he would like to see clarity in the rules governing access to the Jerusalem holy site at the center of the tensions.

The hilltop compound is a frequent flashpoint and its fate is a core issue at the heart of the Israeli-Palestinian conflict.

It is the holiest site in Judaism, revered by Jews as the Temple Mount, once home to their biblical Temples.

Muslims call it the Noble Sanctuary and believe it is the spot where the Prophet Muhammad ascended to heaven. It is the third holiest site in Islam and houses the Al-Aqsa and Dome of the Rock mosques.

On Friday, Israel lifted restrictions on Muslim worshippers in an apparent bid to ease tensions as Kerry continued his diplomatic push. Israel had barred younger Muslim men — seen by police as the main potential trouble-makers — from entering the compound on Fridays, the main day of prayer in the Muslim religious week. The bans, which were put into place intermittently, had at times targeted men up to the age of 50 and fueled Palestinian fears that Israel is trying to change long-standing understandings under which Jews are allowed to visit, but not pray, at the shrine.

Those fears have also been fueled by a rise in visits to the shrine by Jewish activists demanding prayer rights, including senior members of Netanyahu's coalition government.

Israel has repeatedly denied Palestinian allegations that it is trying to change the status quo and accused Palestinian political and religious leaders of lying and inciting to violence.