Abdullah and Abbas are meeting Monday in Ramallah.
The king supports Abbas' Palestinian National Authority and the "efforts to achieve peace and establish an independent Palestinian state on the 1967 borders based on the two-state solution," the Jordan News Agency Petra reported.
The 1967 reference is to Israel's borders before a war that year that led to Israeli occupation of the West Bank and Gaza.
Jordan is one of three Arab League members to recognize Israel.
The meeting comes four days before Abbas, of the Palestinian Fatah party, is to meet with rival Hamas party leader Khaled Mashal in Cairo to work out details of a new unity government that would close a six-year schism between the factions that has politically separated the West Bank from Gaza.
Palestinian Prime Minister Salam Fayyad said Sunday he would resign if the Fatah and Hamas parties agree to reconcile. Fayyad's stepping down was a key Fatah demand for reconciliation.
Israel warned a Fatah-Hamas agreement would have grave consequences for Israeli relations with the Palestinian Authority, both in terms of security and the transfer of tax and customs revenues, which Israel collects under a 1994 agreement.
"The prime minister [Binyamin Netanyahu] has said repeatedly, the Palestinian Authority must choose between peace and Hamas -- they cannot have both," an Israeli official told Britain's Guardian Sunday.
"Our security cooperation with the Palestinian Authority, for example, has been based on the commitment of both sides to fighting terrorism. If Hamas is in the government, what will this mean?" the official said.
Israel and the United States classify Hamas as a terrorist organization.
Hamas is also a steadfast opponent of the Palestinian Authority's efforts to reach a peace deal with Israel, a state it refuses to recognize.
Deputy Secretary of State William Burns, the highest ranked U.S. foreign service officer, met with Abbas in Ramallah Sunday evening to discuss Washington's opposition to the reconciliation.
He was to meet with Netanyahu in Jerusalem Monday.
Washington criticized a provisional Fatah-Hamas deal reached in May and threatened to cut funding if the reconciliation was carried out.
The United States is one of the Palestinian Authority's biggest donors, giving more than $3.5 billion since the authority was established in 1994.