Najib Mikati spent Thursday trying to form a new government after the coalition government of Saad Hariri was dissolved following a Hezbollah-led opposition walkout earlier this month.
Hariri's Future Movement party called on Mikati to meet its obligations to the international community and back the Special Tribunal for Lebanon, which is investigating the 2005 assassination of former Prime Minister Rafik Hariri, the Saad Hariri's father.
A memo from the Future Movement to Mikati calls on the presumptive leader "to commit not to agree to a request for the cancellation of memos of understanding Lebanon has signed with the United Nations or to a request to freeze the Special Tribunal for Lebanon," Lebanon's Daily Star newspaper reports.
Hezbollah was upset over the continued support for the tribunal. It's widely expected the Shiite movement will be named by the tribunal for the slaying, though Hezbollah, which threw its support behind Mikati, said the STL is a political tool of Israel.
Mikati, who considers himself a moderate, said he would seek a consensus agreement on the STL. Hariri said he wouldn't take part in a government that is under the influence of Hezbollah.
Hezbollah said it wasn't trying to take control of power in Beirut.