The Local Coordination Committees of Syria said 23 of the dead were in the opposition stronghold of Homs, CNN reported.
Syrian forces attacked a bridge on the Orontes River near the border with Lebanon, the Syrian Observatory for Human Rights said.
Dana Suleiman, a spokesman for the U.N. High Commissioner for Refugees in Beirut, said at least 2,000 Syrians have fled into Lebanon since Sunday.
U.S. Gen. James Mattis, head of the U.S. Central Command, told a Senate Armed Services Committee hearing President Bashar Assad's forces remain viable.
"He will continue to employ heavier and heavier weapons on his people," Mattis said. "I think it will get worse before it gets better."
Meanwhile, Syria agreed to let the top U.N. relief official and newly designated U.N.-Arab League envoy Kofi Annan visit.
Valerie Amos, the U.N. undersecretary-general for humanitarian affairs and emergency relief, said the Assad regime gave her permission to visit Syria for three days starting Wednesday.
The regime had refused for a month to let Amos visit.
She said she intended "to urge all sides to allow unhindered access for humanitarian relief workers so they can evacuate the wounded and deliver essential supplies."
The International Committee of the Red Cross -- the only relief agency permitted in Syria -- said Monday a Red Cross and Syrian Arab Red Crescent convoy arrived in the hard-hit central-western city of Homs.
It was helping two areas of the city but was prevented by Syrian troops from entering the devastated Baba Amr neighborhood, held by rebels for several months before regime forces drove them out Thursday after nearly four weeks of relentless shelling, the ICRC said.
Troops loyal to the Assad regime have sealed Baba Amr, citing security problems.
Amos said she planned to leave Damascus Friday.
Her visit was to be followed Saturday by Annan, a former U.N. secretary-general appointed last week as a special representative to Syria for the United Nations and the Arab League.
At the same time, Syrian security forces widened their campaign to crush opposition, activists said.
Troops fought army defectors in Daraa, a southwestern city 62 miles south of Damascus, activists said.
Daraa is where the anti-regime protests began a year ago and was the first city besieged by Syrian forces.
Syrian forces also bombarded the western-central city of Rastan, 12 miles north of Homs, Monday, activists said.
Notable deaths of 2014 [PHOTOS]