The meeting in Amman came hours after fresh clashes broke out in east Jerusalem where Israeli police fired tear gas, percussion bombs and rubber bullets to disperse Palestinian demonstrators.
Months-long unrest in annexed east Jerusalem has in recent days spread to the occupied West Bank and Arab communities across Israel, raising fears of a new Palestinian uprising.
The meeting between Abbas and Kerry, who arrived in Jordan late yesterday, came a day after Israel approved plans for another 200 settler homes in annexed east Jerusalem - a move sharply criticized by Washington.
Much of the unrest in Jerusalem has been fuelled by Israeli moves to step up settlement activity in the city's eastern sector and by religious tensions at the Al-Aqsa compound, a site holy to both Muslims and Jews.
Earlier, a tense confrontation erupted in the city's Issawiya neighborhood as about 100 residents, including schoolchildren, tried to block a main road after police closed off several neighborhood entrances with concrete blocks.
The Palestinians have also been infuriated by a far-right Jewish campaign for prayer rights at the Al-Aqsa compound, although Israel insists it has no plans to change the decades-old status quo.
Israel's Public Security Minister Yitzhak Aharonovitch said the authorities were on alert for more unrest, after several attacks in recent weeks by Palestinians wielding knives or ploughing cars into pedestrians.
"I believe there will still be terror attacks and other incidents in the near future," he said.
Abbas's spokesman said the Palestinian leader was expected to tell Kerry of his growing concerns over Israel's actions, particularly in Jerusalem.
In a letter to the UN Security Council sent yesterday, Palestinian ambassador Riyad Mansour demanded international intervention over Al-Aqsa, warning that tensions could "spiral out of control".