Locals have reported "intense gunfire" after troops and tanks moved into the city from several directions at dawn.
The army is signalling that it will not tolerate large-scale unrest ahead of the month of Ramadan, when protests are expected to grow, correspondents say.
Syria has seen more than four months of protests against the rule of President Bashar al-Assad.
Centre of protests A doctor in Hama told Reuters news agency that the death toll was rising rapidly, putting the latest estimate at 24.
He said the city's Badr, al-Horani and Hikmeh hospitals had received 19, three and two dead bodies respectively.
"[Tanks] are firing their heavy machineguns randomly and overrunning makeshift road blocks erected by the inhabitants," he said by phone, with machinegun fire in the background.
Residents of northern Hama, where the attack seemed to be concentrated, said tank shells were falling at the rate of four a minute there. They also confirmed deaths in the area.
Electricity and water supplies had been cut, they said, in a tactic regularly used by the military when storming towns to crush protests.
The government blames armed Islamist gangs for the unrest, but correspondents say the protests appear largely peaceful, with only isolated cases of residents arming themselves against the military assault.
Significance of HamaHama - a bastion of dissidence - occupies a significant place in the history of modern Syria. In 1982, then-President Hafez al-Assad, father of Bashar, sent in troops to quell an uprising by the Sunni opposition Muslim Brotherhood. Tens of thousands were killed and the town flattened. The operation was led by the president's brother, Rifaat.
Similarly, current President Bashar Assad has turned to his own brother, Maher, who commands the army's elite Fourth Division, to deal with the unrest.
Hama, with a population 800,000, has seen some of the biggest protests and worst violence in Syria's 2011 uprising.
Activists say more than 1,500 civilians and 350 security personnel have been killed across Syria since protests began in mid-March. More than 12,600 have been arrested and 3,000 others are missing.
The protests show no sign of letting up despite a government crackdown that has brought international condemnation and sanctions.
On Saturday, troops shot dead three people who threw stones at a military convoy sent to quash unrest in the eastern city of Deir al-Zour, the Syrian Observatory for Human Rights said.
Spokesman Rami Abdel Rahman said about 60 military vehicles, including tanks, personnel carriers and trucks crammed with soldiers deployed in the key oil hub, which has seen near daily protests.
A total of 20 people were killed and 35 wounded on Friday as hundreds of thousands of protested in cities across Syria, rights groups said.
More than 500 people were arrested in a single operation in the Qadam neighbourhood of the capital Damascus, they added.