A protester ready to throw a stone during rioting in Beirut
The US has said it is backing Lebanese efforts to form a new coalition amid rising tension sparked by the killing of security chief Wissam al-Hassan.
US state department spokeswoman Victoria Nuland warned a power vacuum would pose a great risk to stability, reports the BBC.
"The export of instability from Syria threatens the security of Lebanon now more than ever," she said.
Deadly clashes erupted in Beirut and Tripoli after opposition figures blamed Syria for the attack on Gen Hassan.
"We support the efforts of President Michel Suleiman and other responsible leaders in Lebanon to build an effective government and to take the necessary next steps in the wake of the terrorist attack," Ms Nuland told reporters.
"It's up to the Lebanese people to choose a government that is going to counter this threat. In the interim, we don't want to see a vacuum."
She added that US Ambassador Maura Connelly was due to meet Lebanese politicians to discuss the possible shape of the new coalition.
Meanwhile, European Union foreign policy chief, Catherine Ashton held talks in Beirut with President Suleiman and Prime Minister Najib Mikati on Tuesday.
She also warned against the dangers of a political vacuum and welcomed efforts to "maintain stability through national dialogue".
"Such acts of terrorism are designed to provoke reaction and to create tensions," Ms Ashton said.
"The importance of robust state institutions that continue to ensure security and provide services cannot be understated."
Gen Hassan, who headed the intelligence branch of the Internal Security Forces, was killed in a car bomb blast on Friday, along with one of his bodyguards and a woman nearby.
The senior official was a Sunni and an outspoken critic of Syrian President Bashar al-Assad.
He also maintained close links to the Western-backed 14 March opposition bloc and the family of its leader, former Prime Minister Saad Hariri.
Gen Hassan's murder has led to deadly clashes between pro- and anti-Syrian factions. As a result, the Lebanese army has been deployed on the streets of Beirut and Tripoli to try to stem the violence.
Over the weekend, President Suleiman rejected an offer of resignation from Mr Mikati - a Sunni Muslim at the head of a cabinet dominated by the pro-Syrian Shia Islamist movement Hezbollah and its allies.
The decision prompted ex-Prime Minister Fouad Siniora to warn: "The Lebanese people won't accept, after today, the continuation of the government of assassination."
Thousands attended Gen Hassan's funeral on Sunday, which became a political rally against both Mr Mikati and Syria.
Police scuffled with a group of protesters who attempted to storm the prime minister's office, and overnight into Monday protesters set up road blocks in Beirut, prompting exchanges of gunfire.
On Monday, dozens of people set up camp outside Mikati's office, calling for his resignation.
Opposition MPs boycotted Tuesday's parliamentary sessions.
The army has urged "all political leaders to be cautious when expressing their stances and opinions" and in attempting to mobilise public action "because the fate of the nation is at stake".
The military is a widely respected institution in Lebanon that has often been required to stand between the country's diverse political and religious factions.