"The Egyptian proposal rejects isolating Syria and calls for achieving stability in the region and not opening a new focus of tension that adds to an already complicated situation," Egyptian presidential spokesman Suleiman Awad said on Sunday.
He was speaking to reporters after talks in Cairo between Egyptian President Hosni Mubarak and his Syrian counterpart Bashar al-Assad.
The United States has warned Syria that it faces isolation unless it cooperates with Iraq over border security.
Syria says it has deployed thousands of troops on the Iraq border to prevent infiltrators entering Iraq.
Washington has also accused Syria of drawing up an assassination hit list targeting Lebanese political leaders, a charge Syrian officials deny.
Many Lebanese go further and blame Damascus for al-Hariri's assassination, which Demascus also denies.
A UN team investigating al-Hariri's death, led by Detlev Mehlis, finished questioning several Syrian officials last week and will report its findings in late October.
Mubarak is "calling upon Syria to go on cooperating with Mr Mehlis. He is against any finger pointing at Syria before Mr Mehlis's report is made available to the United Nations," Awad said.
"The Egyptian proposal rejects isolating Syria and calls for achieving stability in the region and not opening a new focus of tension that adds to an already complicated situation"
Egyptian presidential spokesman
The official Syrian Arab News Agency reported that al-Assad briefed Mubarak on the visit of Mehlis to Damascus and also discussed "the cooperation offered by the Syrian authorities so that his mission is successful".
Diplomats in Damascus say Syria has been seeking to rally Arab support to ease US pressure on it.
Some Arab media have reported an Egyptian-Saudi initiative that would include Syrian concessions on political reform and increased border security.
Asked if any joint initiative existed, Awad said: "I am always reluctant to talk about initiatives or mediation. What I am talking about is ongoing, continuing efforts exerted by President Mubarak of Egypt in order to bring this whole situation to an early conclusion."