The Red Cross has expressed alarm over the situation in the besieged Syrian town of Qusair, and has appealed for immediate access to deliver aid.
Thousands of civilians are believed to be trapped as pro-government forces battle rebels, with medical supplies, food and water scarce.
Russia earlier blocked a UN “declaration of alarm” on Qusair.
In Syria on Sunday, at least three people were reportedly killed by a car bomb in a Damascus suburb.
The blast, in the district of Jobar, appeared to target a police station, according to the UK-based pro-opposition Syrian Observatory for Human Rights.
Reuters news agency quoted a Lebanese security source on Sunday as saying that at least 15 people were also killed in overnight fighting between Hezbollah fighters and Syrian rebel forces in Lebanon’s eastern town of Baalbek. The casualties have not been independently verified.
An opposition activist told the BBC on Friday that around 30,000 civilians were still in Qusair, which is close to the border with Lebanon.
Rebel-held parts of Qusair are effectively blockaded by government forces and Hezbollah fighters.
The International Committee of the Red Cross (ICRC) said in a statement it was “alarmed” by reports of civilians trapped in Qusair and was prepared to enter the town immediately to deliver aid.
Civilians and the wounded are at risk of paying an even heavier price as the fighting continues,” said the head of the ICRC’s operations in the region, Robert Mardini.
The UN secretary general’s office also appealed to the warring parties to allow residents to flee.
The BBC’s Imogen Foulkes in Geneva says the fact that both the UN and ICRC have issued urgent statements at the same time is an indication of how desperate they believe the situation has become.
However, a draft UN Security Council declaration, which was circulated by Britain, voicing “grave concern about the situation in Qusair, and in particular the impact on civilians of the ongoing fighting”, was blocked by Russia.
Council statements such as these must be agreed unanimously.
A diplomat said Russia blocked the draft text because the UN had failed to speak out when Qusair was seized by rebels.
Fighting in Qusair intensified last month with militants from Hezbollah joining forces loyal to President Bashar al-Assad.
Reinforcements from the rebel Free Syrian Army are reported to have managed to break through from the north-east to support the embattled rebel fighters.
Some Lebanese Sunnis have also crossed into Syria to fight alongside the rebels, who are drawn largely from Syria’s majority Sunni community.
Braced for offensive
On Saturday, influential Muslim cleric Yusuf al-Qaradawi called on Sunni Muslims from around the Middle East to join the battle against President Assad.
He told a rally in Doha that Iran and Hezbollah, Mr Assad’s main allies, wanted to exterminate Sunnis.
Activists from the Syrian Observatory for Human Rights say rebels in Qusair are bracing themselves for another assault.
Fifteen Syrian army tanks have massed north of the town, says Rami Abdel Rahman, the observatory’s director.
“Regime forces are reinforcing the sites that they have north of the city, including Dabaa airport and Jawadiya,” he said.
Qusair, which lies 10 km from the Lebanese border, is considered a key logistical hub and supply route for weapons smuggled into Syria.
The town is also located near the main road connecting the city of Homs to the Syrian capital Damascus.