U.S. Secretary of State Hillary Clinton said Tuesday that a Hizbullah-controlled government in Lebanon would "clearly have an impact" on ties with the United States.

The comments came after Hizbullah-backed Najib Miqati was named Lebanon's prime minister-designate, giving the Iran- and Syria-backed armed group increased leverage in the deeply divided country to the anger of many Sunnis.

The Mustaqbal movement condemned on Tuesday the manner in which Najib Miqati was appointed prime minister-designate, saying: "It does not make him a consensual premier, but one that has been imposed on the Lebanese by Hizbullah."

It said in a statement read by former minister Jean Oghassabian: "This practice has destroyed what was left of Lebanon's free democratic system and the bloc affirms that democracy cannot be rectified through weapons."

Prime Minister-designate Najib Miqati on Tuesday rejected attempts to cast him as "Hizbullah's man" and said the dispute over a U.N. tribunal that brought down his predecessor could only be resolved through dialogue.

"Don't prejudge me or my behavior, please, especially the international community," the 55-year-old billionaire businessman told Agence France Presse in an interview at his Beirut home shortly after being appointed to form a new government.

The arrest warrants in the Hariri murder would be activated "in cooperation with the government of Beirut, which is obligated to extradite -- if necessary with the help of other states," Special Tribunal for Lebanon Registrar Herman von Hebel has said.

In an interview with the online version of German weekly Der Spiegel, von Hebel said it is likely the names contained in the arrest warrants will be made public in "six to 10 weeks" and that a trial could start as soon as the beginning of September.

Free Patriotic Movement leader MP Michel Aoun condemned on Tuesday the protests against the appointment of Najib Miqati as prime minister-designate, saying: “Today’s events have taken place between those seeking to burn the city and those seeking to build it.”

He assured the Lebanese after the movement’s weekly meeting that they will witness financial and economic relief with Miqati’s appointment, hoping that all sides would cease their sectarian incitement.

Hizbullah Secretary General Sayyed Hassan Nasrallah noted on Tuesday that Lebanon is going through a critical and difficult phase that requires responsible action, adding that the opposition “seeks the cooperation of all sides in order to overcome this phase.”

He stressed that the opposition has confronted developments and the indictment through constitutional means.

The Muftis council in Lebanon, headed by Grand Mufti Mohammad Rashid Qabbani, urged on Tuesday Prime Minister-designate Najib Miqati to “thwart strife in Lebanon in light of the parliamentary consultations to form a new government in Lebanon.”

It called on him to “take the appropriate stand that would avert strife and prevent Lebanon from falling into chaos and the trap of the conspiracy being devised against the Lebanese, and Muslims in particular.”

Protests turned violent on Tuesday in Lebanon's Sunni bastion of Tripoli as frenzied demonstrators torched an Al-Jazeera van while protesting the likely appointment of a Hizbullah-backed premier.

Angry demonstrators set upon the vehicle, smashing the windshield and tearing down the satellite dish before setting it on fire.

Prime Minister-designate Najib Miqati must form a new Lebanese government without outside "interference," France's foreign ministry said on Tuesday.

"It is essential that it is done within the framework of the constitution ... and reflects the independent and sovereign choice of the Lebanese people, without any interference and through dialogue," it said.

The top-ranking U.S. envoy for the Middle East, Jeffrey Feltman, said he would travel to France on Wednesday for talks on the situation in Lebanon and Tunisia, following a visit to Tunis.

"I'm going to meet with the French tomorrow to talk about Tunisia and Lebanon," he told reporters in Tunis.