Syrian troops have reportedly crossed into Lebanon in armoured cars to battle armed opposition fighters with rocket-propelled grenades.
The news agency Reuters said the Syrian army had advanced into the country on Tuesday, destroying some buildings in a hunt for rebels.
Around 35 Syrian soldiers "came across the border and started to destroy houses" said one resident in the rural area of al-Qaa.
Reports of continued violence emerged from across the country, including claims by the New York-based Human Rights Watch that the Syrian armed forces were using civilians as "human shields" in Idlib.
The report said that troops were forcing civilians to march in front of the advancing army to retake areas that had been under the control of the rebels.
View Syria 27 March 2012 in a larger map
Above: the region where violence between Syrian troops and rebel fighters was reported.
Despite the reports, Syria was reported to have "accepted" Kofi Annan's six-point plan for a cessation of violence, which was recently endorsed by the UN Security Council.
UN and Arab League special envoy Kofi Annan drew up the plan following a visit to Syria last month.
Annan was in China on Tuesday to seek the country's support for the proposal, after gaining Russian president Dmitry Medvedev's backing in Moscow.
He told Chinese premier Wen Jiabao that Syria had reached a "critical juncture". He also told reporters that Syria had accepted the plan but that measures needed to be taken to implement it in practice.
"I indicated that I had received a response from the Syrian government," Annan told journalists. "And will be making it public today, which is positive, and we hope to work with them to translate it into action."
China and Russia had previously vetoed UN resolutions sanctioning President Assad for his role in the crackdown, which the UN says has killed at least 8,000 people since March 2011.
Above: Annan arrives in China to ask for Premier Wei Jiabao's support in the peace deal
The plan does not call on Assad to leave power, but details the need for a Syrian-led political process to "address the legitimate aspirations and concerns of the Syrian people".
It also calls for an immediate end to the fighting, and a halt on the use of heavy weapons in civilians areas, as has increasingly been seen in Homs, Idlib, Aleppo and other major Syrian cities over the past few months.
A daily two-hour "humanitarian pause" to allow aid to reach badly affected areas, freedom of movement for journalists, the release of political prisoners and respect for the right to peacefully demonstrate are also part of the plan.
The Syrian state media network Sana appeared to confirm that Assad had accepted the plan, but did so by calling on opposition fighters to respect the ceasefire when imposed.
It quoted Chinese Foreign Ministry Spokesman Hung Li as saying: "We hope that all the Syrian sides will be able to join the mediation efforts exerted by Annan to ensure the conditions for a political settlement for the situation in Syria."
President Assad was also reported on Tuesday to have visited the Baba Amr region of Homs, which was devastated in almost four weeks of government shelling in January and February.