Amr Moussa, the secretary-general of the Arab League, said earlier this month that direct talks should not resume without "written guarantees".
Tribunal fears in Lebanon
The Saudi king will travel to Damascus on Thursday for a meeting with Bashar al-Assad, the Syrian president, before on Friday travelling to Jordan and on to Lebanon for a series of meetings with political leaders.
Al-Assad is expected to accompany Abdullah on his trip to Lebanon, where both men are scheduled to meet Saad al-Hariri, the Lebanese prime minister.
The Lebanon visit is aimed, in part, at reducing tensions over the Special Tribunal for Lebanon, the UN-backed body investigating the murder of Rafiq al-Hariri, the former Lebanese prime minister.
Hezbollah revealed last week that members of the group would be implicated in the assassination, an announcement that sparked fears of renewed sectarian violence in Lebanon.
Saad al-Hariri urged the public to remain calm in a speech on Saturday.
Al-Hariri's March 14 coalition is closely allied with Saudi Arabia, while the March 8 opposition bloc - which includes Hezbollah - has strong ties with Syria.
This would be the Syrian president's first trip to Lebanon since 2005, before the al-Hariri assassination. The murder has been widely blamed on Syria, but Damascus has routinely denied involvement.