Opposition sources and a Western diplomat stated Mr Assad was in the coastal city of Latakia, directing the response to the assassination of his top lieutenants, according to Reuters.
Mr Assad, who has not made a public appearance since Wednesday’s bombing, was said to be commanding the government operation but it was not clear whether Assad travelled to the Mediterranean Sea resort before or after the attack.
“Our information is that he is at his palace in Latakia and that he may have been there for days,” said a senior opposition figure, who declined to be named.
David Cameron, the prime minister called on Mr Assad to give up power to avert more chaos and bloodshed. Speaking during a visit to Afghanistan, Mr Cameron said: “I have a very clear message for President Assad. It is time for him to go.
“It is time for transition in the regime. If there isn’t transition it’s quite clear there’s going to be civil war.”
Gen Daoud Rajha, the defence minister, Gen Hassan Turkmani, assistant to the vice-president and head of the crisis cell, and Assef Shawkat, the husband of Mr Assad’s sister have been confirmed as casualties of the attack and a number of other senior leaders were injured.
Major Gen Robert Mood, head of the UN monitoring mission, warned that the violence was spiralling, as President Assad appeared to have gone to ground.
Security forces loyal to President Assad pounded rebel hideouts in Damascus on Thursday in retaliatory attacks for the blast that killed three top anti-insurgency leaders.
Hundreds fled Damascus flashpoint districts amid a surge of fighting following a bomb attack which killed three security chiefs, as residents reported shops closed and food shortages.
The troops used helicopters and heavy artillery against the rebels, while snipers took up positions on rooftops on the outskirts of the city, the Syrian Observatory for Human Rights said. “Explosions are heard throughout the capital,” it said.
“The regime has gone mad,” Rima Flaihan, spokeswoman for the Local Coordination Committees in Syria, said in a telephone interview today from Jordan.
She said at least 200 people were killed across Syria yesterday. “The regime is in a horrid state of savagery, seeking revenge for the killings of the military leaders,” she added.
The military gave residents 48 hours to leave areas where clashes are taking place between security forces and rebels who have launched the “Damascus Volcano” offensive ahead of the start of Ramadan fasting on Friday.
“These extremely violent clashes should continue in the next 48 hours to cleanse Damascus of terrorists by the time Ramadan begins,” a security official said.
The bomb attack that killed three top security chiefs in Damascus marks “the beginning of the end of the regime” of President Assad, an opposition spokesman said on Thursday.
“We see that what happened (on Wednesday) is a sign of the beginning of the end of the regime,” Syrian National Council spokesman George Sabra.
“It was a major blow to (Assad) and the regime’s repressive security apparatus.”
The Syrian Observatory for Human Rights watchdog said that in the western district of Mazzeh alone, hundreds of people were on the move, “fearing a large-scale operation by regime troops.”
Meanwhile the Israeli defence minister, Ehud Barak said Syria’s alliance with Iran and Lebanon’s Hizbollah was weakened by the attack.
“The blow is a severe one,” said Barak on a tour of the Israeli-occupied Golan Heights, a day after a blast tore through Syria’s national security headquarters, killing the defence minister and two other top officials close to President Bashar al-Assad.
“It’s also a severe blow to the radical axis, to the Iranians and Hizbollah, who are the sole supporters of the Assad family,” he said in remarks communicated by his spokesman.
The minister said it was possible to watch the battle playing out less than a kilometre (half a mile) away in the Syrian village of Jebata al-Khashab.
“We can see the actual fighting, the mortars, hear the bullets between the Syrian army to rebels or the opposition,” he said.
“This shows how the disintegration (of the Assad regime) is not abstract, it is real, it’s approaching, and what happened yesterday in Damascus will expedite the downfall of the Assad family,” he said.
The FSA, which had predicted an imminent “surprise” on the eve of the attack, claimed that its assault on the capital, named “Damascus Volcano”, would take them to the verge of victory.
“This is the volcano we talked about; we have just started,” said Qassem Saadedine, the group’s spokesman. “We have smashed the inner circle of Bashar,” another rebel official boasted.
A government sources said Assad’s mother and sister have gone to Tartus province for the funeral of his brother-in-law Assef Shawkat who was killed in Wednesday’s Damascus bomb.
“Anissa al-Assad, the widow of (ex-president) Hafez al-Assad and her daughter Bushra travelled on Wednesday evening along with several women from their entourage to Latakia and they then made their way to Tartus.”