Opposition leaders did not say whether they would meet the president again
Talks between President Mikhail Saakashvili and opposition leaders in Georgia have failed to make progress on ending the country's political turmoil.
Statements from both sides indicated their ideas were completely opposed.
The opposition has held a month of mass protests in Tbilisi demanding that Mr Saakashvili step down immediately, four years before his term is due to end.
Critics accuse him of bungling the brief conflict with Russia last August and restricting democratic rights.
Street clashes and an abortive army mutiny last week raised fears of wider unrest in Georgia, which is also hosting Nato military exercises.
On Monday, Mr Saakashvili held talks with four members of the opposition coalition - Irakli Alasania, Levan Gachechiladze, Salome Zurabishvili and Kakha Shartava - for the first time since the protests began on 9 April.
Afterwards, the president said that although the meeting had ended without a breakthrough, both sides had agreed to continue the dialogue. The opposition leaders did not say whether they would.
Mikhail Saakashvili's opponents say he mishandled the war with Russia
"We have a completely different view, the opposition and the president," said Mr Gachechiladze, the main opposition candidate in last year's presidential election. "The protests will continue today and tomorrow, and for a long time."
Ms Zurabishvili, a former foreign minister, said: "Clearly we don't have the same appreciation of reality. Our visions and our paths do not intersect."
Mr Alasania acknowledged that deep differences remained, but said the meeting represented an important first step.
"It was very important to discuss this in person with the president," the former UN envoy added.
Mr Saakashvili also said both sides had "agreed on the fact that it is a step forward, that the dialogue should be continued".
"I have no illusions that we will reach agreement on all issues," he said in a nationally televised address.
Parliamentary Speaker Nino Burdzhanadze, a former ally of the president and now among his fiercest opponents, declined to attend the talks. She earlier repeated her call for the president to resign.
More than 10,000 people attended a protest outside the parliament building in Tbilisi on Saturday, again calling for Mr Saakashvili's resignation. A smaller crowd of around 3,000 gathered on Sunday.
The demonstrations have so far been mostly peaceful, although on Wednesday they turned violent when a number of protesters clashed with police outside a police station. Several people were injured.
Meanwhile Nato military exercises centred around the Vasiani military base outside Tbilisi got under way on Monday.
Soldiers from 14 different countries, nine of them Nato members, lined up on the parade ground at Vasiani as a band played the Georgian national anthem.
On Sunday, Russian Prime Minister Vladimir Putin said the exercises "cannot be seen as anything other than support for the ruling regime".
Mr Putin said the manoeuvres represented a "step backwards" in US and Russian efforts to "reset" their relations.
A Nato spokesman conceded to the BBC on Monday that relations with Russia were going through a "bumpy period".