Syrian officials say the army have taken control of key points in the the city centre.
According to opposition activists, government troops are being supported by militants from the Lebanese Hezbollah movement.
More than 30 people are reported killed, mostly civilians hit by shelling.
Qusair and the surrounding area are seen as an important piece in Syria's sectarian jigsaw.
For the government it would guarantee access from Damascus to the coast.
Opposition sources say should President Assad fall in Damascus, Syria's coastal region could serve as an enclave for his Alawite sect with the country fragmenting on ethnic and sectarian lines.
Qusair is also important for the rebels because of the access it provides to Lebanon.
The UN in Syria has called on the government for better protection for United Nations staff when they try to bring humanitarian aid to areas controlled by rebels.
"The delivery of medical supplies to the opposition-held areas remains unresolved. This is a protection issue and one of utmost importance," said the UN's coordinator in Syria, Adam Abdul Mawla, at a meeting in Damascus.
The Syrian government is wary because it argues aid consignments have ended up in the hands of armed groups rather than civilians. It says it wants to cooperate with the UN to ensure that aid reaches civilians in need.
The UN says the number of refugees in the civil war is swelling by 10,000 a day, and is set to double from 1.5 million to three million by the end of the year.
Source: Euronews
