"It's only natural that questions are raised by this meeting which claims to come from the Syrian street when the Syrian regime gave its protection and media coverage, counting on it to build a civilised and legitimate image," they said.
"Nobody should have given a drop of legitimacy to the regime at the expense of the blood of our martyrs and the suffering of the detained. The committees renew their commitment to the Syrian street."
The United States said the authorisation of the meeting was a "move in the right direction," but that Assad still needs to go further.
Washington saw the gathering as "progress, and something that is new and is important for the democratic process in Syria that we all want to see," said State Department spokeswoman Victoria Nuland.
"We want to see an end of violence," Nuland added, insisting Washington's view of what Assad needs to do has not changed.
US Secretary of State Hillary Clinton has urged a transition to democracy in Syria, saying a regime crackdown on the street protests would not halt the "irreversible shift" toward change.
On Monday, Assad discussed the "legitimate demands of his people, current events and the implementation of reforms," in a meeting with visiting US congressman Dennis Kucinich, official media said.
The London-based Syrian Observatory for Human Rights says 1,342 civilians have been killed since mid-March in the government's crackdown on protesters and that 342 security force personnel have also died.
A key activist and supporter of the protests, Rami Abdel Rahman, said demonstrations calling for Assad's fall and to condemn the meeting were staged on Monday night in several cities around Syria.
Thousands protested in the central city of Homs, in Hama and Deir Ezzor, both to the north of the capital, the northwestern province of Idlib, in Latakia on the Mediterranean coast and in districts of Damascus, he said.
He said there had also been arrests in various parts of the country.
Late Tuesday, he also said tanks and other armoured vehicles had entered the northwestern village of Al-Rami, in Idlib province, while other militant sources said there was shooting there.
The army has already intervened in various places in Idlib to crush demonstrations.
At the Monday meeting, in a Damascus hotel, the dissidents vowed to press ahead with a peaceful uprising.
In a document they called a "pledge," the dissidents vowed to remain "part of Syria's peaceful uprising for freedom and democracy and pluralism to establish a democratic state through peaceful means."
"There are two ways forward -- the first a clear and non-negotiable move to a peaceful transition to democracy which would rescue our country and our people," opposition activist Munzer Khaddam told the meeting.
"The alternative is a road that leads into the unknown and which will destroy everyone," he said.
They also demanded the right to demonstrate peacefully, the release of political prisoners, freedom of the press, the safe return of refugees and moves to prevent foreign intervention.
Anwar Bunni, a prominent human rights lawyer who has recently been released from jail, was positive about the meeting, which brought together people without any party affiliation.
Indeed, the authorities invited the opposition to a meeting to discuss key changes to the constitution amid the deadly wave of unrest that has pitted pro-democracy protesters against security forces since mid-March.
Security forces this week pressed their sweep for dissidents towards Syria's borders, sending some 11,000 refugees fleeing into Turkey and hundreds more into Lebanon.
In Istanbul, Turkish officials said on Tuesday the number of Syrian refugees in Turkey has decreased to 10,757 after several hundred people returned home.
And in Moscow, a visiting Syrian opposition delegation urged Russia on Tuesday to use its diplomatic clout to convince Assad to stop using force against civilians.
Elsewhere, Britain said it summoned the Syrian ambassador on Tuesday to express concerns about reports a diplomat at the embassy had been intimidating Syrians in the country.