For a third day, al-Assad's forces shelled the city of Homs in western Syria early Thursday, the Syrian Observatory for Human Rights reported.
Government troops and rebels have battled on and off for control of the city since the start of the conflict. Twenty people were found dead in Homs on Wednesday, the LCC reported.
North of Homs, in the city of Saraqib, rebels tried to take over government-held positions. Three rebels and a number of government soldiers were killed, the Syrian Observatory said.
Fighting between rebels and regime forces continued in and around the town of Maaret al-Numan in Idlib province, said Abu Abdul Rahaman, who works with an opposition network that documents what the rebels are doing. He spoke to CNN via Skype.
The town is strategically important because it's on an international highway that the government uses to send supplies to Damascus, Idlib, Hama, Homs and Aleppo.
U.S. observers to Jordan
The United States deployed troops to Jordan to help monitor Syria's stockpile of chemical weapons and determine what efforts to take if violence spreads to neighboring nations, the U.S. defense chief said.
The announcement follows recent news that al-Assad's forces moved some of the weapons for security reasons. Reports have emerged that rebels are focusing their efforts on capturing some of the storage sites.
"We continue to be concerned about security at those sites," U.S. Secretary of Defense Leon Panetta said Wednesday after a meeting of NATO ministers in Brussels, Belgium.
"We want to ensure that security is maintained and we want to be very sure that those (weapons) do not fall into the wrong hands."
Roughly 150 U.S. Army special operations soldiers have been working with Jordanian forces to monitor the chemical and biological weapons sites in Syria while trying to determine how to respond should an issue arise, according to the defense chief.
CNN reported in June that U.S. Special Operations Forces were training and advising Jordanian troops on a range of specific military tasks they might need to undertake if unrest in Syria spills into Jordan or poses a threat to that country. That information came from Defense Department officials who did not want to be named.
Panetta now has publicly acknowledged the troop deployment.
"We have a group of our forces there, working to help them build a headquarters and to ensure that we make the relationship between the United States and Jordan a strong one so we can deal with all of the possible consequences," he said.
A senior Jordanian military official denied Panetta's claims, according to the state-run Petra news agency.
The American troops are in the country for an annual training exercise, the official from the Jordanian armed forces general command told the news agency.
The United States also has been working with Turkey as part of its effort to monitor the weapons sites.
Syria is believed to have one of the "largest and most advanced chemical warfare" programs in the Arab world, said Michael Eisenstadt, director of the military and security studies program at the Washington Institute for Near East Policy.