Reacting to reports of hundreds of civilians killed this week, the Syrian National Council (SNC) called for an "emergency UN Security Council session to discuss the regime’s massacres in Zawiyah mountain, Idlib, and Homs, in particular."
It also appealed for an "emergency meeting for the Arab League to condemn the bloody massacres... and cooperate with the United Nations in taking the necessary measures to protect Syrian civilians."
The SNC, a major umbrella group of factions opposed to Assad, reported "250 fallen heroes during a 48-hour period."
It urged the Security Council to declare the cities and towns under attack "'safe zones' that enjoy international protection; and force the regime's forces to withdraw from said areas."
The United Nations estimates that more than 5,000 people have been killed in the crackdown since mid-March.
A White House statement said Assad's regime had "flagrantly violated their commitment to end violence and withdraw security forces from residential areas.
"The United States is deeply disturbed by credible reports that the Assad regime continues to indiscriminately kill scores of civilians and army defectors, while destroying homes and shops and arresting protesters without due process," it said.
"Time and again, the Assad regime has demonstrated that it does not deserve to rule Syria. It's time for this suffering and killing to stop."
France denounced what it said was the "unprecedented massacre," and urged Russia to accelerate talks for a UN Security Council resolution on the crisis.
French foreign ministry spokesman Bernard Valero said: "Everything must be put in motion to end this murderous spiral into which Bashar al-Assad is dragging his people, deeper each day."
Russia has proposed a Security Council resolution that would denounce violence from both sides, which France has called "unacceptable."
Paris instead seeks a resolution that would directly pin the blame for the violence on the regime and threaten strong international sanctions on Damascus.
Turkish Foreign Minister Ahmet Davutoglu expressed hopes that the Arab League will succeed in its primary aim, which is to stop the bloodshed.
A British foreign office spokesman urged Syria "to end immediately its brutal violence against civilians."
At least 22 people were killed on Wednesday in clashes in the southern province of Daraa, where the protests against Assad's regime erupted in March, the Syrian Observatory for Human Rights said.
"Twenty-two people -- six deserters, a civilian and 15 members of the armed forces and security forces -- were killed and several dozen civilians were wounded in their homes," it said.
For its part, state news agency SANA said two people were killed and seven others wounded in Homs, including a colonel whose legs had to be amputated.
It said one man died and six people were wounded when an "armed terrorist group" attacked a bus. Meanwhile, the driver of an army bus was also killed.
On Tuesday, the Britain-based Observatory said Assad's forces carried out a "massacre" by killing 111 civilians in the northwestern town of Kafruwed, taking that day's civilian toll to 123.
In addition, at least 100 army deserters were killed or wounded in Idlib in the north on Tuesday, the Observatory said, adding that 14 security force members were killed in Daraa province.
More than 100 deserters and civilians were also reported killed on Monday.
Amid the violence, Assad ally Tehran said five Iranian engineers working at a power plant project in Homs were abducted on Tuesday and demanded their "immediate release."
Syrian opposition figures have accused Tehran of aiding Assad's regime in its deadly crackdown.
The latest violence comes as an advance Arab League team prepares to head to Damascus on Thursday to pave the way for some 500 observers.
"Since Syria signed the protocol, it has been fully committed to facilitating the mission of the Arab League which will come to see the reality of the crisis," foreign ministry spokesman Jihad Makdisi told AFP.
"Unfortunately, the Syrian opposition is trying to sabotage the protocol and is seeking to push for foreign intervention rather than accept the call to dialogue," he added.
UN leader Ban Ki-moon called on Syria to give "full cooperation" to the observer mission, his spokesman said.
The mission is part of an Arab peace plan endorsed by Syria on November 2, which also calls for withdrawal of the military from towns and residential districts, a halt to violence and the release of detainees.
Syria blames the unrest on "armed terrorist groups."