Syrian troops have clashed with rebels in the capital, Damascus, and the second city, Aleppo, as they try to retake areas out of their control.
In Aleppo and Homs, there have been revolts and attempted breakouts by prisoners. Nine inmates died during the Aleppo jail rebellion, activists say.
Activists say security forces are threatening to storm the Homs prison.
The renewed fighting comes amid strong international concern over Syria's threat to use chemical weapons.
Damascus said on Monday that such weapons would not be deployed inside Syria but would be against foreign attack.
Explosions and fires have been reported from the Homs jail, where unarmed policemen are said to have defected and prisoners have staged a sit-in. The Syrian Observatory for Human Rights said two prisoners had been killed.
The activist group the Local Co-Ordination Committee (LCC) said there was a "catastrophic humanitarian situation" inside the jail.
The group said the military was planning a massacre and called for international help to prevent "mass executions" of prisoners.
Government officials had earlier denied there had been a defection.
Syrian state television says the government has now regained control of most areas of Damascus which had been captured by rebels last week.
It has broadcast footage of the southern district of Nahr Isha, showing the bodies of "terrorists" it says were killed in the fighting.
Footage showed Syrian troops going from house to house searching for rebel fighters in recaptured areas of Damascus.
Civilians in the Qabun area of the city complained of not being able to leave their homes. Government forces were said to have taken up positions in the Midan district, held earlier by rebels.
The rebel Free Syrian Army (FSA) launched a new offensive in Aleppo, Syria's commercial centre, at the weekend, and fighting is reported to be continuing as pro-government troops attempt to take back the seized districts.
Heavy shelling and rocket fire continued overnight. The BBC's Wyre Davies, on the Turkish border with Syria, says losing Aleppo would be a serious blow to the government so it is determined to use its far superior weaponry to halt the rebels' advance.
The Observatory says more than 1,260 people have been killed in Syria since Sunday, which would be the bloodiest week of the 16-month uprising.
Chemical use 'reprehensible'
On Monday, US President Barack Obama warned Syria's President Bashar al-Assad that his government would be held accountable if it used chemical weapons, saying such a move would be a "tragic mistake".
UN Secretary General Ban Ki-moon said that any thought of using chemical weapons would be "reprehensible".
The sharp international response came hours after Syrian foreign ministry spokesman Jihad Makdissi gave Damascus's first implicit acknowledgement that a chemical weapons stockpile existed.
The US and Israel have expressed concern about the fate of Syria's arms, with Israeli PM Benjamin Netanyahu speaking of a "great threat" of weapons sites falling into the hands of Lebanon's Shia Islamist group Hezbollah, allied to President Assad.
The state department in Washington said any possible use of such weapons would be "completely unacceptable".
The FSA said on Tuesday that the government had moved its chemical weapons stockpile to airports on Syria's border, in an attempt to put pressure on the international community.
"According to our information, the regime began moving its stocks of weapons of mass destruction several months ago," it said in a statement quoted by the AFP news agency.
Meanwhile, the refugee crisis is escalating both inside and outside Syria.
An estimated 1.5 million people are homeless within the country, according to the Syrian Arab Red Crescent. Another 115,000 Syrians have fled to neighbouring countries.
On Sunday, the Syrian Observatory for Human Rights reported that at least 19,106 people had been killed since March 2011. The UN said in May that at least 10,000 people had been killed.
Syria blames the violence on foreign-backed "armed terrorist gangs".
In June, the Syrian government reported that 6,947 Syrians had died, including at least 3,211 civilians and 2,566 security forces personnel.