It was the monarch's first trip to Ramallah since 2017, coming days before Ramadan, historically a period of increased tension between the Palestinians and Israel.
"We and the Palestinians are closer to each other, and are in the same trench," Jordanian state television quoted the king as saying.
King Abdullah is in regular contact with Mr Abbas, but previous meetings have taken place in Amman, not Ramallah, the seat of the Palestinian Authority.
The Palestinian Authority warned this month that Israel must prevent incursions into Al Aqsa mosque during Ramadan, if it "wants to prevent friction."
Jordan is regarded as the custodian of Al Aqsa and of other holy places in Jerusalem.
The kingdom has been seeking a more high-profile role in the region since the November 2020 election of US President Joe Biden. Jordanian officials believe his predecessor Donald Trump side-lined the kingdom, especially when dealing with the Palestinian-Israeli conflict.
The visit is part of continued discussions with Mr Abbas “to confront all the challenges regarding many issues of concern" to the two men, said the official Palestinian news agency.
Mr Abbas has a de facto second headquarters in Jordan, where he regularly meets Arab and western officials.
King Abdullah met leaders from Iraq, Egypt and the UAE in the port city of Aqaba last week.
Jordanian state television said on Monday that Jordan was making efforts to support Palestinians by "finding a political horizon to meet all their legitimate rights on the basis of a two-state solution”.
A large proportion of Jordan's 10 million people are of Palestinian origin.
Jordanian officials have been increasingly critical of Israel's actions against the Palestinians, which they say could eventually prompt another migration of Palestinians to Jordan after two refugee waves in 1948 and 1968.