Lebanon's outgoing premier Saad Al-Hariri on Thursday asked his Hezbollah-backed successor to clarify his position on a UN tribunal probing the killing of Hariri's father before deciding on whether to join the new cabinet.

MP Fouad Siniora, of Hariri's Future Movement, said prime minister-designate Najib Mikati was asked during talks with Hariri to state clearly whether his government would cease all cooperation with the Special Tribunal for Lebanon (STL).

"We asked the prime minister-designate to clarify his position (concerning the tribunal) and to mention that clearly in his policy statement," Siniora, himself a former premier, said.

Siniora said Mikati was asked to say whether he would stop Lebanon's share of funding for the Netherlands-based court, remove the three Lebanese judges on the STL and renounce the protocol of agreement concerning the court.

An official from Hariri's party said that once Mikati clarifies his position, the Future Movement would decide its stance on the new government.

"We asked him to clarify these things. Once he does, we'll see," he said, requesting anonymity.

The tribunal, set up in the aftermath of the 2005 assassination of ex-premier Rafiq Al-Hariri, was at the heart of a dispute that led Hezbollah and its allies to topple Hariri's government two weeks ago.

Hezbollah believes that the court stands to implicate some of its members in Hariri's killing.

Mikati said this week in an interview with AFP that he hoped to resolve the dispute over the tribunal through dialogue, and acknowledged that Lebanon could not force the tribunal to stop its work.

He added, however, that the country's cooperation with the STL was another question altogether, without elaborating.

Michel Aoun, leader of the Christian Free Patriotic Movement allied with Hezbollah, told reporters on Thursday after meeting Mikati that what was being asked of the new premier was to end all cooperation with the tribunal.

"We cannot stop the tribunal's work, but what we are asking is that Lebanon cease its cooperation with the court," Aoun said.

Mikati on Thursday began the difficult task of forming a new government, meeting with parliamentary blocs before reporting back to President Michel Sleiman on Friday.

He has said he would seek to form a cabinet that includes all parties, but Hariri's Western-backed coalition has flatly rejected joining a government headed by a candidate they deem was imposed by Hezbollah.