There have been clashes throughout the night in many parts of Syria, after the deaths on Wednesday of three top regime figures in a suspected suicide attack.
Government and opposition both said large numbers of people died, in one of the bloodiest days of the conflict.
Activists said artillery and helicopters were used in the worst attack, on a funeral south of Damascus.
The president's brother-in-law, defence minister and head of Mr Assad's crisis team died in yesterday's bombing.
Rebel groups said the bomb had been planted the day before the meeting at national security headquarters where it was detonated.
They predicted the government's imminent fall.
The army has pledged to rid Syria of "criminal and murder gangs".
The London-based Syrian Observatory for Human Rights said on Thursday that more than 150 people had died across the country on Wednesday, in one of the worst days of a 16-month revolt.
The BBC's Jim Muir, in Beirut, says that video of one attack posted on the internet showed scenes of pandemonium after what activists said was a helicopter gunship attack on a funeral procession at Sitt Zeinab, south of the capital.
They said at least 60 people were killed in this incident alone.
In Damascus, state media said, security forces launched operations in many areas which have been clashes in recent days, mainly in the south-west and north-east, killing many "terrorists".
Activists reported more tanks moving towards the capital from the west.
Following Wednesday's bombing, the government has vowed to root out ruthlessly what it describes as armed terrorists backed by outside powers.
But our correspondent says the rebels are on the offensive too, warning state TV and radio to evacuate their personnel before its headquarters comes under attack.
In contrast with earlier explosions in Damascus, there were no photos or video from the scene of Wednesday's blast at the security headquarters and the BBC's Lina Sinjab said no windows in the building appeared to be broken.
Among the victims were
Defence Minister and ex-chief of staff Gen Daoud Rajiha
Deputy Defence Minister Assef Shawkat, married to Mr Assad's sister Bushra
Assistant to the vice-president and head of crisis management office Gen Hassan Turkomani
Two other senior officials - interior minister Mohammad Ibrahim al-Shaar and National Security Bureau chief Hisham Ikhtiar- were wounded
The US said the killings were a major blow to the regime.
"I think the incident today makes clear that Assad is losing control," White House spokesman Jay Carney told reporters.
"All of our partners internationally need to come together to support a transition."
UK Prime Minister David Cameron said Mr Assad should step down and that it was "time for transition in the regime".
In Lebanon, Hezbollah leader Hassan Nasrallah condemned what he termed a targeted killing: "We are going to miss them and we offer our condolences to the Syrian leadership and the Syrian army."
Russia said some countries had incited the opposition rather than calming it down.
The attack prompted the UN Security Council to delay until Thursday a vote on a Western-sponsored resolution calling for tougher sanctions on Damascus.
UN Secretary General Ban Ki-moon said the Security Council must "shoulder its responsibility and take collective and effective action.
"Time is of the essence.
The Syrian people have suffered for too long.
The bloodshed must end now," Mr Ban said.
The mandate for the UN's observer mission runs out on Friday.
The resolution before the Security Council would extend the mission and place international envoy Kofi Annan's peace plan under Chapter 7 of the UN Charter, which could ultimately authorise force.
But Russia is firmly against harsher measures.
In a telephone conversation between President Barack Obama and President Vladimir Putin on Wednesday, the two leaders were said to be divided in their approaches to ending the bloodshed.