The Thursday night shootings came a day after Assad told U.N. Secretary-General Ban Ki-moon that military and police operations had stopped, according to a statement issued by the United Nations.
More protests were expected across Syria after noon's prayers Friday as the oppositions called for demonstrations through social media.
Rami Abdul-Rahman, who heads the London-based Syrian Observatory for Human Rights, said there was wide security deployment in many parts of the country as well as army's armored personnel carriers in some areas. Citing witnesses in the areas, Abdul-Rahman added that army checkpoints were present as usual in the northwestern region of Jabal al-Zawiya in Idlib province.
The shootings were accompanied by a wave of arrests in several parts of Syria, including the suburbs of the capital Damascus and the central city of Homs. Despite the crackdown thousands of people protested Thursday night demanding Assad's ouster, activists said.
"Shooting was heard in Homs Friday morning," Abdul-Rahman said.
The observatory and The Local Coordination Committees, a group that documents anti-regime protests, said one person was killed in a Damascus suburb. Another died of his wounds early Friday in the central city of Homs.
Assad is coming under mounting criticism for his assault on a 5-month-old uprising. Human rights groups and witnesses accuse Syrian troops of firing on largely unarmed protesters and say more than 1,800 civilians have been killed since mid-March.
In a stinging written statement, President Barack Obama said Thursday that Assad has overseen a vicious onslaught of his people as they protest for freedom. It was Obama's first explicit call for Assad to step down.
Obama said Assad's calls for reform ring hollow while he is "imprisoning, torturing and slaughtering his own people." Obama also signed an executive order that gives his administration authority to impose sweeping new sanctions on Syria intended to further isolate Assad.
The leaders of France, Britain and Germany issued a statement saying Assad should "leave power in the greater interests of Syria and the unity of his people." In a report released in Geneva, a U.N. team said the violence in Syria should be referred to the International Criminal Court. Crimes against humanity are considered the most serious of all international human rights violations after genocide.
The U.S.-based Physicians for Human Rights applauded Obama's decision to call on Assad to step down and called for accountability for human rights violations "The US Administration took a strong stand in solidarity with the Syrian people. ... the U.S. is trying to create real political space for the Syrian people to determine their future," said Hans Hogrefe, PHR Washington Director and Chief Policy Officer.
"However, the widespread human rights violations and the many deaths caused by the brutal crackdown cannot be absolved by a simple resignation. Instead, there must be full accountability for the perpetrators."