Activists say Syrian security forces have killed at least 13 people as thousands of protesters rallied across Syria Friday to test the government's acceptance of an Arab League peace initiative.

Syrian state television denied there were killings. Government officials say they have offered amnesty to anyone who surrenders weapons in the coming days.

But U.S. State Department spokeswoman Victoria Nuland Friday advised Syrians not to turn themselves in to the authorities.

Members of anti-government groups say forces killed most of the people in Homs and the suburbs of the capital, Damascus. According to the anti-government groups, government forces had starting shooting at demonstrators in several towns shortly after the weekly Friday protests began.

Earlier this week, the Arab League brokered a plan to halt violence and convene talks between the government and the opposition.

The plan called for Syrian authorities to immediately withdraw security forces from the streets, stop violence against demonstrators and release all detainees jailed since protests began.

But opposition groups continue to voice their skepticism over the government's offer of peace. Activists blamed pro-government forces for at least 12 deaths on Thursday in Homs.

In Cairo Thursday, members of the opposition Syrian National Council met with the Arab League chief to discuss the way forward. Council member Samir al-Nashar said the group did not discuss possible dialogue with the Syrian government but instead asked that Mr. Assad step down. The SNC then offered to “engage in negotiations” to move from an authoritarian government to a democratic one.

The United Nations says the number of people killed during the eight-month-old uprising against Mr. Assad has topped 3,000.

The Syrian government has blamed much of the unrest — including deadly violence in Homs this week — on “terrorists” and gunmen.