"I believe there should be some sort of a summit meeting and also a forum of the U.N. Security Council," Shevardnadze said after his meeting.
He said he pledged his full cooperation and solidarity with President Bush in his efforts to gain international support for the U.S. campaign against terrorism in the wake of the Sept. 11 terrorist attacks on New York and Washington.
"I must add that this was my first meeting with President Bush, and he's left me with absolutely great impression, with his erudition, his knowledge, his determination to end terrorism," Shevardnadze said.
The Georgian leader who met separately with Vice President Dick Cheney had agreed earlier this week to allow the United States access to airspace over the Black Sea in its possible military strikes against Afghanistan. He said Friday, however, that he did not think the United States was going to have massive strikes.
Shevardnadze was a former Soviet foreign minister whose reforms contributed to the end of the Cold War. He was also foreign minister when Soviet forces invaded Afghanistan in December 1979.