The United Nations Security Council, including Russia and China, has agreed to a statement on Syria that backs a bid by the UN-Arab League envoy Kofi Annan to end the violence.
In a statement approved by all its 15 members, the council threatened Syria with unspecified further steps if it fails to comply with Mr Annan's peace plan.
The proposal calls for a ceasefire, political dialogue between the government and opposition, and full access for aid agencies.
The original statement was diluted at Russia's demand, editing out any specific ultimatums.
The conflict spilled over Syria's borders late on Wednesday when several shells hit the Lebanese border village of al-Qaa and nearby fields, injuring one person, residents said.
The village, 10 km from the Syrian border, has been the first stop for many of the 7000 Syrian refugees who have fled fighting into Lebanon.
Refugees complain that they are pursued by Syrian forces, who have often fired across the border, but al-Qaa residents said this was the first time artillery has been used.
Adding to the pressure on Damascus, European Union governments are set to impose sanctions on Assad's wife Asma on Friday, EU diplomats say.
The sanctions, which still need formal approval from ministers, would mean she will no longer be able to travel to the 27-nation bloc or buy products from EU-based shops in her own name.
The British-born former investment banker became the focus of media attention when a trove of emails obtained by Britain's Guardian newspaper appeared to show her spending tens of thousands of dollars on internet shopping sprees while Syria descended into violence.
At least 8,000 people have died in the revolt, according to United Nations figures.