The statement noted that the summit followed a call by the Saudi monarch for inter-Arab reconciliation made at an Arab economic summit in Kuwait City in January.
The gathering was designed to mark a thaw in relations between Syria on the one hand and Saudi Arabia and Egypt on the other after years of differences over Damascus' links to Iran and Hezbollah, a Lebanese Shia organisation.
Relations between Riyadh and Damascus had been further damaged in the wake of the 2005 assassination of Rafiq al-Hariri, a former Lebanese prime minister, who had close ties to the Saudi government.
Interim reports from a UN investigation into al-Hariri's killing alleged that Syrian officials had a hand in the plot, claims consistently denied by Syria.
With the al-Hariri case now under the auspices of a special tribunal in The Hague, Saudi Arabia is looking to unite regional powers before the Arab League summit in Doha, the Qatari capital, set to take place on March 30.
Marwan Bishara, Al Jazeera's senior political analyst, said that the meeting in Riyadh is an attempt by each of the leaders to address political changes affecting the region.
"Usually on the eve of most Arab League summits we find that Arab leaders, especially those from Saudi Arabia, Syria and Egypt, try to work out and manage their differences in order to come out on top in the Arab League summit and give a good impression of their regional behaviour," he said.
"This time, there is something more serious. The region has been changing over the last few years; there is a new administration in the US and it seems that there could be a radical right-wing government in Israel.
"That regional change is enticing each one of these three Arab leaders to enhance their position in order to be an indispensable party to any decisions."
In a parallel development, Egypt, with the support of Saudi Arabia, is brokering talks in Cairo between the rival Palestinian groups, Hamas and Fatah.
Fatah is led by Mahmoud Abbas, the Palestinian president.
Israel lists Hamas as a "terrorist organisation" and has so far only held talks with Fatah.
The meeting in the Egyptian capital is aimed at forming a national unity government for the Palestinians that can eventually engage in peace negotiations with Israel.
The Arab League summit in Kuwait in January left Arab countries split over Israel's 22-day assault on the Hamas-controlled Gaza Strip, with Syria and Qatar adopting a more strident tone than Egypt and Saudi Arabia.
More than 1,300 Palestinians were killed during the war, which Israel said was aimed at preventing rocket fire from Palestinian fighters based in the coastal strip.
The Saudis have since tried to get all 22 Arab states to support a fresh push for the 2002 Arab Peace Initiative for Israel and the Palestinians.
The plan offers Israel recognition from all Arab states in return for the establishment of a Palestinian state based on borders before the 1967 Arab-Israeli war and the principle of right of return for Palestinian refugees.
The Saudis have repeatedly called on Washington and Israel to support the plan, stressing that it will not be indefinitely on offer.
"Israel must realise that the choice between peace and war will not be available all the time, and that the Arab initiative on the table today will not be on the table forever," King Abdullah said at the Kuwait summit.