In his third address to the nation since protests began, he said Syria should deal with people's demands for reform but that a "small faction" was exploiting popular grievances.
He said a national dialogue would shape Syria's future and urged people who had fled to Turkey to return.
Rights groups say at least 1, 300 civilians died in protests since March.More than 300 soldiers and police have also been killed, they say.
Meanwhile, thousands of people who fled a military assault in the north-west of the country are now living in refugee camps across the border in Turkey. Some refugees said the army had cut off the border town of Bdama, which had been providing supplies to those fleeing Jisr al-Shugour.
Speaking in a televised address to supporters at Damascus University, Assad expressed regret about the protest deaths, saying that they were a great loss to the nation and him personally. But he said the "saboteurs", who had smeared the image of Syria across the world during the protests, had to be isolated.
"What is happening today has nothing to do with reform, it has to do with vandalism," he said. "There can be no development without stability, and no reform through vandalism." But the Syrian president also said a national dialogue authority was being set up to create a reform plan, and another committee would be created to examine the constitution. Syrian citizens should be involved in combatting corruption at all levels, he added. He said he had instructed the justice minister to consider expanding a recent amnesty. Assad also called on thousands of people who had fled into Turkey fearing violence to return to their homes "as soon as possible".
He referred in particular to the residents of Jisr al-Shughour, where armed forces recently took control after violence in which more than 100 security personnel were killed."The state will protect them. It is there to protect them," he said.
President Assad's latest speech, his third since the unrest began, takes place a day after opposition activists announced the creation of a body to lead the struggle against the regime.
"We announce the creation of a National Council to lead the Syrian revolution, comprising all communities and representatives of national political forces inside and outside Syria," spokesman Jamil Saib told reporters near the Turkish border, according to the AFP news agency.
The council urged people to "co-operate in all cities and provinces of Syria to achieve the legitimate goal of overthrowing the regime and bring it to justice", Saib added. Also on Sunday, activists said the army had surrounded Bdama - only 2km (1.2 miles) from Turkey - with checkpoints and was stopping people attempting to head for the Turkish border. Nonetheless, hundreds have managed to escape.
Assad's recent appearances
* 30 March: In address to parliament, described unrest as conspiracy against Syria by its foreign enemies
*16 April: In TV address, announces end to emergency law, expresses sadness over deaths and calls for national dialogue
More than 10,000 Syrian refugees have crossed the Turkish border, and Turkish officials say another 10, 000 are sheltering on the Syrian side.
The local Turkish governor's office said some Syrians were collecting food at the border to take to the stranded families. The governor's office said there was no question of Turkish soldiers crossing into Syria.
Raka al-Abduh, 23, told AFP that his family fled Bdama on Saturday but he went back on Sunday morning to get bread. He reached the village using mountain routes and found it all but abandoned. "They closed the only bakery there. We cannot get bread any more," he said. "I saw soldiers shooting the owner of the bakery. They hit him in the chest and the leg."
There were also protests overnight in the cities of Hama, Homs, Latakia, Deir al-Zour, Madaya, and several suburbs of Damascus, activists said.