0115 GMT January 24, 2018
In his first visit to Abbas's headquarters in Ramallah in five years, Abdullah was welcomed on a red carpet near his helicopter by the Palestinian leader before the two national anthems were played, AFP reported.
The two men did not address the media but shook hands with senior Palestinian officials.
The visit came less than two weeks after the end of a standoff at the Al-Aqsa Mosque compound in Beit-ul-Moqaddas where Israel had imposed new security measures, including metal detectors, following a gunfight that killed two Israeli policemen and three Palestinians.
Jordan, which is the custodian of the site, reacted angrily to the new measures, while Palestinians responded with days of protests.
The tensions were exacerbated on July 23 when an Israeli security guard shot dead two Jordanians at the Israeli embassy compound in the capital Amman.
The crisis eased on July 27 when Israeli Prime Minister Benjamin Netanyahu ordered the removal of the metal detectors.
Abdullah's visit was seen by analysts as providing support to Abbas, who has been isolated by Israel over his response to the Al-Aqsa row.
The mosque compound is in East Beit-ul-Moqaddas, occupied by Israel in 1967 in a move never recognized by the international community.
Netanyahu's removal of the metal detectors was seen by Palestinians as a victory.
At Abbas's headquarters a large banner was erected with a picture of the Al-Aqsa Mosque compound with the slogan "Jerusalem (Beit-ul-Moqaddas) is victorious."
In a statement on the official state news agency Petra, the king was quoted as saying that without Jordanian "custodianship and the steadfastness of the Jerusalemites, the holy sites would have been lost many years ago."
In the middle of the crisis over the metal detectors, Abbas suspended security coordination with Israel, and it has remained suspended despite their removal.
As such 82-year-old Abbas cannot leave the West Bank as Israel controls the border crossings.