Activists say supporters and opponents of the Syrian government have clashed in several cities, and least seven people have been killed.
Witnesses and human rights activists say Syrian security forces fired on anti-government crowds Tuesday, causing casualties in the central cities of Homs and Hama and the Mayadin district of Deir al-Zour. Demonstrations also erupted in the capital, Damascus.
Anti-government protesters went into the streets after pro-government rallies in which thousands gathered to show support for President Bashar al-Assad.
State television showed tens of thousands of pro-Assad demonstrators in Damascus and other cities, holding flags and pictures of the president, a day after he blamed the recent unrest on "saboteurs" and laid out plans to consider political reforms.
Also Tuesday, the state news service said Mr. Assad has granted a general amnesty for crimes committed before June 20, but did not provide further details.
In the president's 70-minute speech Monday, he offered a national dialogue that would begin to review new laws on parliamentary elections, the media and possible reforms to Syria's constitution.
Activists immediately dismissed his promises, saying they failed to meet the demands of protesters who for three months have rallied for democratic changes and defied a fierce military crackdown.
The International Committee of the Red Cross says Syrian officials have agreed to give the aid group wider access to areas of unrest, which it says is "imperative" to assess the humanitarian situation in the country. The agreement follows meetings between ICRC President Jakob Kellenberger and Syrian Prime Minister Adel Safar.
Turkey is sheltering more than 10,000 Syrians in tent cities near the Syrian border. Turkish officials say another 10,000 who have fled the military crackdown are sheltering close to the frontier just inside Syria.
Rights activists say more than 1,400 civilians have been killed and 10,000 detained since mid-March in the government's crackdown on protests.
Some information for this report was provided by AP and Reuters.