Palestinians rejoice as new restrictions at entrance of holy site, including metal railings, are removed after protests.
Abbas and Abdullah met for about two hours, after a red-carpet welcome for the king at the Palestinian government compound in the city of Ramallah.
Abbas thanked the king for efforts made on behalf of the Palestinians, including during the al-Aqsa crisis, said Abbas spokesman Nabil Abu Rudeineh.
Abdullah expressed support for Abbas and the Palestinians, the spokesman said.
The king’s West Bank visit, his first in five years, comes two weeks since a surge in violence in Jerusalem after Israel installed metal detectors at entrances to the al-Aqsa Mosque compound – Islam’s third holiest site.
Jordan serves as the custodian of the site, which houses the al-Aqsa Mosque and the Dome of the Rock shrine. The western wall of the compound is sacred to Jews.
Abdullah’s role as custodian of the shrine is a key component of his legitimacy.
Al Jazeera’s Scott Heidler, reporting from West Jersualem, said the two leaders agreed to form a crisis committee over the al-Aqsa compound.
“They say there is a habitual encroachment by Israeli forces on the Al-Aqsa compound. And they want to work closer together to deal with future crises, which they say are inevitable because of the way Israel is dealing with the issue.
“Moving forward, they are going to form a committee. They also said they will better coordinate and come up with a better plan when it comes to communications over the Al-Aqsa compound.”
The crisis erupted when Israel installed metal detectors at the shrine after gunmen killed two Israeli policemen there. The gunmen were Palestinian citizens of Israel.
The restrictive measures triggered protests by Muslims, which forced Israel to remove the devices.
Abbas suspended security ties with Israel over the crisis.
In a separate incident last month, an Israeli security guard at Israel’s Amman mission compound killed a Jordanian teenager who he accused of attacking him. A bystander was also killed in the shooting.
King Abdullah harshly criticised Israeli Prime Minister Benjamin Netanyahu for warmly welcoming the security guard, who flew back to Israel.
Israeli police say an investigation into the deaths is being conducted.
“The Israeli prime minister has to adhere to his responsibilities and take the legal measures that guarantee the killer’s trial instead of dealing with this crime in a political, showyámanner aimed at making personal political gains,” Abdullah said last month.
Since the embassy shooting, Abdullah has said he would donate $1.4m to the Muslim administration of the shrine.
Separately, Abbas has said his self-rule government in the occupied West Bank will allocate $25m to improve services for Palestinians in Jerusalem.