"We reject any dialogue while tanks shell our towns, snipers shoot our women and children and many areas are cut off from the world by the regime without electricity, communications or water," Hadi Abdullah, a resident of the bombarded city of Homs, said on Thursday night.
Another activist told Reuters that Annan's call for dialogue sounded "like a wink at Bashar" that would only encourage Assad to "crush the revolution".
Annan, a former UN secretary-general, has been entrusted by the Arab League and the UN to find a peaceful resolution in Syria.
He cautioned against military intervention in the country earlier on Thursday, saying it risks making the conflict worse.
On Friday morning, clashes erupted in Homs province, the DPA news agency reported.