Some 200 delegates taking part in the dialogue, including independent MPs and members of the Baath party, in power since 1963, observed a minute's silence in memory of the "martyrs" before the playing of the national anthem.
But opposition figures boycotted the meeting in protest at the government's continued deadly crackdown on unprecedented protests that erupted in mid-March against President Bashar al-Assad.
"We are going to hold a comprehensive national dialogue during which we will announce Syria's transition towards a multi-party democratic state in which everyone will be equal and able to participate in the building of the nation's future," Vice President Faruq al-Sharaa said in his opening address.
He said that within a week the interior ministry would implement a government decision to "remove all obstacles to any citizen returning to Syria or travelling abroad.
"Circumstances have prevented the full implementation of several laws promulgated recently, including that ending the state of emergency," in force for five decades, the vice president said.
"We need to recognise, however, that without the sacrifices made by the Syrian people who have shed blood in more than one province, this meeting could not have been held."
Dissident writer Tayyeb Tizini, who was among the few figures close to the opposition to join the meeting, expressed regret that the government had not halted its crackdown on major protest centres ahead of the dialogue's launch.
"The bullets are still being fired in Homs and Hama. I would have hoped that that would have stopped before the meeting. That's what's necessary," Tizini told delegates.
He also called for the release of thousands of detainees.
Activists said at least one person was shot dead by security forces in Homs on Sunday after tanks rolled into several districts of the central city.
SANA said the foreign ministry summoned the US and French ambassadors to hear "a strong protest against their visit to Hama without prior authorisation... which constitutes a flagrant interference in Syria's domestic affairs."
In Washington, a senior US official denied that the US envoy had been summoned and accused Damascus of orchestrating violent protests over the weekend at the American embassy.
Both US envoy Robert Ford and French ambassador Eric Chevallier visited Hama on Thursday amid repeated large demonstrations in the city.
The French foreign ministry, meanwhile, summoned Syria's ambassador to France on Sunday to hear a "vigorous protest" over damage done to the French embassy and a consulate in Syria.
Syrian demonstrators caused the damage on Saturday after the French ambassador's visit to Hama.
The demonstrators who gathered at the French embassy in Damascus and the consulate in Aleppo burned French flags, threw projectiles into the compounds, destroyed vehicles and generally caused "considerable damage", the ministry said.
SANA said Assad on Sunday named Anas Naim as the new governor of Hama after firing Ahmad Khaled Abdel Aziz on July 2, a day after huge anti-regime protests labelled the largest ever.
A Facebook call for nationwide demonstrations against taking part in the dialogue proposed by Assad brought hundreds of thousands back onto the streets on Friday. For a second time, nearly half a million protested in Hama alone.
Security forces killed at least 15 people on Friday and arrested more than 200 during the anti-dialogue protests, activists said.
The London-based Syrian Observatory for Human Rights, citing activists in Idlib province in the northwest, said the military entered Maala and Shanan villages and damaged the houses of wanted militants and burned motorcycles.
"Security forces overnight Saturday and on Sunday arrested 25 people and beat others in areas south of Banias" on the coast, it added.
Human rights groups say that since the anti-regime protests first broke out, the security forces have killed more than 1,300 civilians and made at least 12,000 arrests.
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