Hama residents told The New York Times shelling resumed in the early morning as people were going home from mosques after dawn prayers.
At least three people were killed, activists said.
The opposition Local Coordination Committees reported two other deaths elsewhere in the country.
Dozens were killed in Hama Sunday; some estimates of the toll reached 150.
A doctor in Hama told CNN hospitals are overwhelmed with the wounded and said security forces are deliberately attacking people who try to help.
Snipers on rooftops kept many staff members from getting to hospitals, he said.
Another doctor said the dead are being buried in gardens, parks and back yards because it is impossible to get to cemeteries.
Turkey joined the chorus denouncing the regime of President Bashar Assad Monday.
"We were greatly frustrated and disappointed about the operation in Syria yesterday, especially in Hama," Foreign Minister Ahmet Davutoglu said. "We strongly condemn these operations."
The call for a Security Council meeting followed condemnations by the United States, European Union and United Nations and an appeal from Lebanon for the Arab world to end its "silence" on the crackdown.
The dawn-to-dusk assault the day before the holy month of Ramadan, when activists vowed to hold nightly anti-regime protests, was condemned as the broadest and fiercest crackdown yet by Assad's government.
Activists described a massacre after armored units, ending a monthlong siege, smashed through makeshift barricades around Hama and other cities.
They said the massacre was carried out by troops and security agents accompanied by busloads of irregular militiamen known as Shabiha, or "Ghosts," who are part of the same Alawite Shiite minority group as the Assad family.
Human-rights groups said the death toll in Hama alone could reach 150, the English-language Daily Star of Beirut, Lebanon, reported.
More than 1,000 people were reported wounded in the simultaneous raids on several Syrian cities, and the lives of people being treated at Hama's al-Horani Hospital were feared in danger as security forces stormed the hospital, the Coordination Committee of Syrian Peaceful Revolution told Dubai's Gulf News.
International media are still largely banned from Syria, but video clips posed on YouTube by Sham, a Web site sympathetic to the protesters, showed unarmed civilians taking cover from shelling and heavy machine-gun fire as hospitals struggled to cope with mounting casualties.
Bodies lay scattered on the streets, residents said.
"They started shooting with heavy machine guns at civilians, at the young men protecting the barricades," activist Omar Habal told Britain's The Guardian.
Sham said some soldiers in Hama and the northeastern city of Deir al-Zour on the Euphrates River deserted from the forces assaulting the cities.
The official Syrian Arab News Agency said two security-force members were killed in Hama and three in Deir al-Zour.
U.S. President Barack Obama described the government bloodshed as "horrifying," demonstrating "the true character of the Syrian regime."
He said Assad showed he was "completely incapable and unwilling to respond to the legitimate grievances of the Syrian people."
"In the days ahead, the United States will continue to increase our pressure on the Syrian regime, and work with others around the world to isolate the Assad government and stand with the Syrian people," Obama said in a statement that did not demand Assad step down, as he has with Libyan leader Moammar Gadhafi.
EU foreign affairs and security policy chief Catherine Ashton said the brutal attacks were "even more unacceptable coming on the eve of the holy month of Ramadan."
"The Syrian army and security forces have the duty to protect citizens, not to massacre them indiscriminately," she said.
U.N. Secretary-General Ban Ki-moon also condemned the violence, urged Assad to heed Syrians' aspirations and reminded "Syrian authorities that they are accountable under international human rights law for all acts of violence perpetrated by them against the civilian population."
Former Lebanese Prime Minister Saad Hariri "condemned" the Ramadan eve "massacre" and urged other Arab leaders to end their "silence" on the crackdown by refusing to condemn Syria's "bloody" onslaught.
The Syrian people deserve "to define their choices freely and within their humanitarian rights," Hariri said in a statement.
Syria, which borders Lebanon to the north and east, occupied Lebanon from 1976 through April 2005.
Lebanon, a current non-permanent member of the U.N. Security Council, did not immediately respond to the German and Italian calls for an emergency closed-door council session likely to take place Monday afternoon.
Western European countries proposed a resolution condemning Syria's crackdown June 8, but China and Russia, both Syrian allies, threatened to veto it.