The Syrian Observatory for Human Rights said seven people, including a child, died in "intensive shelling" that targeted the Homs neighbourhood of Baba Amr, while the Khaldiyeh and Karm al-Zaytoun sectors were also blitzed.
Activists have said that in the past few days the regime has been bolstering its forces outside Homs, apparently to storm the city after 18 straight days of siege.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
The Observatory, a Britain-based monitoring group, said heavy shelling for two hours early Tuesday of Khaldiyeh and Karm al-Zaytoun later gave way to more sporadic attacks.
The group also reported that Syrian security forces opened fire overnight to disperse a demonstration in Damascus, as daring protests spread in the stronghold of President Bashar al-Assad's regime.
Security forces opened fire at demonstrators who took to the streets in the capital's Al-Hajar Al-Aswad neighbourhood overnight, the Observatory said.
Protesters during the night also blocked the roads leading to Baramkeh Square in the centre of the capital, according to Mohammed Shami, a spokesman for activists in Damascus province.
He said demonstrators used "burning materials" to shut the roads, triggering a security alert that saw "heavily armed forces" deployed in the area in few minutes.
The demonstrators were acting as part of a "campaign of civil disobedience in Damascus in support of Homs and afflicted Syrian cities," Shami said in a statement.
The Red Cross said Monday it was in talks with the Syrian authorities and rebels to halt the violence so that it can deliver aid, amid calls to allow women and children out of Homs.
Attacks in the battered city claimed 12 of the 24 people killed -- 19 civilians and five soldiers -- across the country on Monday, according to reports by the Syrian Observatory for Human Rights and state media.
Assad on Monday again accused foreign parties of funding and arming rebels to destabilise his country.

