Thousands of Syrian government forces, backed by helicopters, are reported to be advancing on rebel forces in the second city of Aleppo.
Turkish officials, meanwhile, have announced that border gates with Syria are being closed to trucks in response to the intensifying violence.
The pro-opposition Syrian Observatory for Human Rights said fighting raged in Aleppo overnight and into the morning on July 24-25.
Also on July 25, activists said Syrian forces fired artillery and rocket barrages into a northern Damascus suburb, forcing hundreds of families to flee.
The government offensive comes after four senior regime security officials were killed and others injured in a rebel bomb attack last week in central Damascus.
In Turkey, Customs and Trade Minister Hayati Yazici said border gates with Syria will be closed to trucks unless they are travelling on to third countries.
By stopping trucking across the 911-kilometer border, the move deprives Syria of a main route for imports and exports.
Syrian rebels recently seized control of two gates on the Syrian side of the frontier.
The United Nations' refugee agency (UNHCR) said Turkish authorities have told the agency that Turkey's borders with Syria will close to commercial traffic but remain open for Syrian refugees fleeing the conflict.
UNHCR spokeswoman, Sybella Wilkes, said the UN agency received assurances from Turkey that "the border is closed for all commercial traffic in both directions."
Reports say that more than 42,000 Syrian refugees who have fled the violence have been accommodated in camps near the border in Turkey.
Chemical Weapons Fears
In another development on July 25, Russia's deputy foreign minister says Moscow has received "firm assurances" from the Syrian regime that its chemical arsenal is safe.
Gennady Gatilov told the ITAR-TASS news agency that "the security of this arsenal is fully safeguarded."
Gatilov also said Russia is conducting the "relevant urgent work with the leadership of Syria so as to ensure reliable protection of the country's chemical weapons storage places."
He did not elaborate.
Syrian Foreign Ministry spokesman Jihad Makdissi acknowledged on July 23 that the country had chemical weapons.
The spokesman pledged that embattled President Bashar al-Assad's regime would not use the arms against its own population, but only if attacked by an outside force.
Western countries and Israel have expressed fears that Syria's chemical weapons could be obtained by militant groups.
With reporting by AP, ITAR-TASS, and Reuters