"We came to find a solution," Alloush said after arriving, adding however: "There is no common ground with the regime. The regime wants to eliminate the opposition."
The Syrian government and its ally Moscow consider the Islamist Army of Islam, or Jaish al-Islam, to be "terrorists" who should not be part of negotiations to end Syria's almost five-year-old civil war.
Other opposition groups have also said it is unacceptable for the High Negotiations Committee (HNC) delegation to be led by a member of an armed group.
Jaish al-Islam, which is opposed to both the government of President Bashar al-Assad and the Islamic State group, is believed to receive wide backing from Saudi Arabia.
The comments came as the HNC held talks in Geneva with the UN special envoy for Syria, Staffan de Mistura, aimed at entering six months of indirect peace talks with Assad's government.
