The United States and the European Union have expressed concern at the political situation in Lebanon, where the opposition has called for the premier to step down over a deadly blast blamed on Syria.
The US says it backs Lebanese efforts to form a new coalition amid the tension sparked by the killing of security chief Wissam al-Hassan.
US state department spokeswoman Victoria Nuland said on Tuesday that a power vacuum would pose a great risk to stability.
"The export of instability from Syria threatens the security of Lebanon now more than ever," she said.
Nuland added that US Ambassador Maura Connelly was due to meet Lebanese politicians to discuss the possible shape of the new coalition.
She added that Washington backed efforts by President Michel Suleiman and other leaders to build an effective government.
"President Suleiman is engaged in discussions with all parties to form a new government," she said. "We support that process."
Also on Tuesday, the EU foreign policy chief Catherine Ashton cautioned against a political vacuum in Lebanon at the end of a visit to the country, where she met Prime Minister Najib Mikati.
Ashton also warned that "there are some who are trying to divert attention from the situation in the region by causing problems in Lebanon," without saying who, Lebanon's National News Agency (NNA) reported.
Her concerns were highlighted when an opposition MP said he and four colleagues had received texted death threats from a Syrian telephone number before and after Friday's car bombing in Beirut.
Ammar Houry, an MP with the fiercely anti-Assad opposition movement of Saad al-Hariri, said on Monday that "on the eve of the attack, we received an SMS from a Syrian number that read: 'Sons of bitches, we will get you one by one'."
They did not pay much attention to it until al-Hassan was killed, he added.
Afterwards, "we received a second SMS that read: 'Congratulations, the countdown has begun. One of 10 eliminated.'"
Al-Hassan's murder has sparked fears of new sectarian strife in Lebanon, where much of the Sunni Muslim community opposes Assad's regime, while Hezbollah, the shia group support him.
Since Friday's bombing, at least 11 people have been killed in fighting between pro- and anti-Syrian camps in the northern city of Tripoli, including a woman who died on Tuesday.
The city is a bastion of anti-Assad sentiment but also home to a minority of Alawites, who belong to the same offshoot of Shia Islam as Assad.
There has also been scattered violence in Beirut since the bombing, with a Palestinian youth killed, but the capital was calm on Tuesday.
Al-Hariri and other opposition figures have blamed Damascus for the assassination of al-Hassan and demanded the resignation of Mikati, whose cabinet is dominated by the Syrian-backed Hezbollah.
Thousands attended Hassan's funeral on Sunday, which became a political rally against both Mikati and Syria.
Al-Hariri, himself a former premier, has said he was determined to oust Mikati's government "by peaceful and democratic means." However, analysts have said that unless Mikati willingly resigns, the government will stay in place.
Mikati expressed a desire to step down but said on Saturday he would stay at the request of Suleiman in the "national interest".