Prime Minister Najib Mikati, a Hezbollah ally, resigned in March because of differences between the March 14 coalition and the March 8 slate, which includes Hezbollah. Ahmad Fatfat, a member of the Future Movement, part of March 14, said Hezbollah was blocking Cabinet developments.
"What right do [Michel] Aoun and Hezbollah think they have to objecting to names put forward by the Future Movement," Fatfat was quoted by the Daily Star newspaper in Lebanon as saying.
Aoun leads the Free Patriotic Movement, allied with Hezbollah. The Daily Star last week said he refused a "take-it-or-leave-it" offer on Cabinet ministers from Prime Minister-designate Tammam Salam.
Hezbollah and its allies said they may quit the government if the issue isn't resolved.
Hezbollah's military support for the Syrian government was blamed by Lebanese security officials for a series of bombings in Lebanon. U.N. Secretary-General Ban Ki-moon has said the escalation of violence was a threat to the country's stability.
Lebanon broke free from Syrian dominance with its Cedar Revolution in 2005. Syria held significance during Lebanon's 25-year civil war, which ended in 1990.