The United States, which has imposed a raft of tough sanctions to try to force Assad's departure, reacted by lifting an asset freeze imposed on Hijab.
"The United States encourages other officials within the Syrian government, in both the political and military ranks, to take similarly courageous steps to reject the Assad regime and stand with the Syrian people," Treasury official David Cohen said.
Hijab's replacement as premier, Wael al-Halqi, insisted the sanctions imposed by Arab and Western governments "have only affected innocent Syrians."
After Damascus talks with UN humanitarian chief Valerie Amos on what she called the "deteriorating humanitarian situation," the prime minister voiced confidence in "Syria's capacity to resist, to overcome the crisis and to bring about reconciliation, security and stability".
Western policymakers hope that a wave of defections will force the collapse of the autocratic government, ending a conflict that seems to be in stalemate with the international community deeply divided over what action to take.
In another blow, rebels claimed Monday they had shot down a Syrian fighter jet and captured its pilot as it battles escalating air attacks by government forces, particularly in the key northern city of Aleppo.
Assad was shaken last month when four top security officials at the heart of his Alawite inner circle were killed in a bomb attack in Damascus claimed by the rebel Free Syrian Army.
"Syria is full of officials and military leaders who are awaiting the right moment to join the revolt," Hijab said, urging the fractured opposition to unite.
Although a number of senior figures have abandoned the regime, analysts say until military units begin to defect en masse, the Assad family and the top echelon of the military and security services will remain intact.
Hijab's comments came as fresh fighting for control of key districts of Aleppo erupted while Syrian forces bombarded areas around Damascus and launched a new security operation in the capital, a human rights watchdog said.
An AFP photographer said he heard heavy shelling of the southwestern district of Saif al-Dawla, which army forces advanced on Monday after recapturing the neighbouring area of Salaheddin last week.
Pro-government daily Al-Watan said the capture of Salaheddin was but a "first step" in the retaking of all rebel-held areas of the city.
The metropolis of some 2.7 million people -- where communications have been cut for at least three days -- is seen as pivotal to the outcome of the conflict, with some referring to it as Syria's Benghazi, the Libyan city at the heart of the revolt that toppled Moamer Kadhafi's regime.
In Damascus, security forces raided several districts after a major security operation on Monday, while several suburbs outside the capital were shelled, according to the Syrian Observatory for Human Rights.
A total of 89 people were killed nationwide on Tuesday, 53 of them civilians, it said.
The opposition issued a new appeal Monday for the international community to impose no-fly zones similar to those established during the conflict in Libya amid increasing air strikes by Syrian warplanes.
"We've seen a very troubling and despicable uptick in attacks from the air, perpetrated by the Syrian regime," Pentagon spokesman George Little told reporters.
Asked if Washington was moving towards enforcing a possible no-fly zone, he said: "We plan for contingencies."
With Assad increasingly under pressure, a top presidential aide was dispatched Tuesday to China, which has said it wants an immediate ceasefire and political dialogue to halt the bloodshed.
China and Russia are at odds with the West over how to end the fighting, after both traditional Syria allies vetoed UN Security Council resolutions.
China said it had backed the peace plan of outgoing peace envoy Kofi Annan, who announced his resignation earlier this month in the face of the continued violence and the deadlock among world powers.
The conflict has killed more than 23,000 people since March last year, according to the Observatory, while the UN says more than one million people have been displaced and another 140,000 have fled to Syria's neighbours.
Damascus also faces isolation by fellow Muslim states as the Organisation of Islamic Cooperation meets in the Saudi City of Mecca to discuss a recommendation for Syria to be suspended from the 57-nation body.
But Iran -- Damascus's closest ally -- is vehemently opposed.
Washington charged Tuesday that Tehran is working to form a pro-regime militia in Syria, similar to the Hezbollah militia it promoted in neighbouring Lebanon during that country's 1975-90 civil war.
"It is obvious that Iran has been playing a larger role in Syria in many ways," US Defence Secretary Leon Panetta told a news conferencce.
"There's now an indication that they're trying to develop, trying to train a militia within Syria to be able to fight on behalf of the regime," he said.