Syrian man cries while holding the body of his son near Dar El Shifa
The number of refugees from Syria may double or even triple this year if the conflict does not end, the UN's refugee chief has said.
Speaking in neighbouring Turkey, Antonio Guterres warned of the "risk of an explosion" across the Middle East if the crisis continued much longer.
Fighting flared up again on Sunday as rebels reportedly launched a surprise attack inside the city of Homs.
As many as 70,000 people have died in the two-year conflict, the UN believes.
More than a million Syrians have now been registered as refugees by the UN in neighbouring countries, reports the BBC.
"If this escalation goes on and nothing happens to solve the problem we might have in the end of the year a much larger number of refugees - twice or three times the present level," Guterres told reporters in Ankara.
He urged countries to help support Turkey, Lebanon, Jordan and other countries sheltering the refugees.
The reports of fighting in Homs on Sunday could not be verified independently.
A UK-based monitoring group opposed to President Bashar al-Assad, the Syrian Observatory for Human Rights, said rebels had launched an attack on the Baba Amr district early on Sunday.
Pro-Assad forces regained control of the district a year ago after fierce fighting.
"The rebels infiltrated Baba Amr during the night," Observatory director Rami Abdel Rahman told AFP news agency.
"Those manning the army checkpoints barely had time to realise what was going on."
Activists later reported government forces had launched strikes on Baba Amr to counter the rebel offensive.
Unverified video said to show fighting in Homs has been posted online. Shooting can be heard and smoke is seen rising over a built-up area.
Reports have also emerged of new air strikes by government forces on the northern city of Raqqa, which was captured by rebels less than a week ago.
According to the Observatory, 14 people died in the bombardment on Saturday.