(CNN) -- The U.S. ambassador to Lebanon is urging "all political factions to remain calm and exercise restraint" after the fall of the government this week.
Maura Connelly, who issued the statement after meeting with parliament member Michel Aoun, on Friday called for the parties "to work together to find a solution for the numerous issues in front of the Lebanese people."
"It is now more important than ever that all sides commit to constructive dialogue and avoid escalating tensions in the country," he said.
Members of the powerful Hezbollah movement and its allies resigned from Lebanon's unity government Wednesday, a move that brought down the government of Prime Minister Saad Hariri.
Lebanese President Michel Suleiman asked Hariri to remain as head of a caretaker administration and requested that Cabinet members continue their duties until a new government can be formed.
He issued a decree scheduling parliamentary consultations to name the next prime minister for Monday and Tuesday. That prime minister will attempt to form the new government.
Hariri's government and Hezbollah had been at an impasse over the investigation by a U.N.-backed special tribunal of the 2005 assassination of Rafik Hariri, the current premier's father.
It is widely expected the tribunal will indict members of the Shiite Muslim Hezbollah, which is designated as a terrorist organization by the U.S. State Department.
The failure to reach a breakthrough has raised fears of a renewal of the sectarian bloodshed that plagued Lebanon in 2008.
Connelly said the United States will continue to work with Hariri "as head of Lebanon's caretaker government on all of the issues of vital importance in the U.S.-Lebanese bilateral relationship." Also, it will continue to support Lebanon's institutions through military, security and economic development aid.
"The United States continues to support the Special Tribunal for Lebanon as the Lebanese people's best hope for putting its tragic and bloody history of political violence behind it," she said.
"As the United States and the international community have said from the beginning, the STL is an irrevocable, international judicial process; its work is not a matter of politics but of law. The resignation of some of Lebanon's ministers will not change this."
The Lebanese Constitution stipulates that the president must hold consultations with members of parliament -- individually or by parliamentary blocs -- to name the candidates for prime minister. The candidate who gets the most votes or nominations is then named prime minister and asked to form a government.
Rafik Hariri's death stunned the nation and prompted tens of thousands to protest, blaming neighboring Syria for the killing. Syria has always denied the accusations. At the time of the bombing, Syria had immense political influence in Lebanon.
A U.N. Security Council resolution demanded Damascus fully cooperate in the investigation. Eventually, the horrific events and the probe led to a complete withdrawal of Syrian troops from Lebanon after 30 years of military presence.