Shara delivered a message from President Bashar al-Asad during his meeting with Mubarak in Egypt's Red Sea resort of Sharm al-Shaikh on Tuesday.
The message dealt with "the consultations underway to overcome what happened in Tunis and to prepare the Arab summit so that it leads to results capable of overcoming the challenges facing the Arab world", said an unnamed source.
Egypt is seeking to rally support for the summit, which was originally scheduled for Monday, to be held as soon as possible after it was called off at the 11th hour by its hosts in the Tunisian capital.
Tunisia has said it still retains the right to host the event, after Egypt stepped in with an offer to hold the summit in Cairo where the Arab League has its headquarters.
According to an Arab diplomatic source in Riyadh, Shara was due to travel on to Riyadh for further consultations on the postponed summit.
Amid the diplomatic flurry following the Tunis fiasco, Mubarak held talks in Sharm al-Shaikh late on Monday with Bahrain's King Hamad. And Saudi Crown Prince Abd Allah bin Abd al-Aziz is expected there on Wednesday.