Pro-government crowds in Syria have given Russian Foreign Minister Sergei Lavrov a hero's welcome in the capital.
Syrian and Russian flags were waves as his convoy moved through Damascus.
Meanwhile, Government forces continued a fierce assault on rebels in Homs. Hundreds are reported to have died since the shelling began on Friday.
Mr Lavrov's office says Russia is seeking "swift stabilisation of the situation in Syria".
He said Mr Assad would soon announce a date for a referendum on a new constitution.
He also says the president is ready for dialogue with all political forces and is interested in an expanded Arab League mission to Syria to monitor the violence.
In a separate development, Gulf Arab states said they were expelling Syria's ambassadors in the region and recalling their own ambassadors in Syria.
The United States closed its embassy in Damascus on Monday and pulled out all remaining staff.
Britain, France, Spain and Italy have already recalled their ambassadors.