A government spokesman revealed on Thursday that the offer of talks was to all parliamentary leaders “to discuss the situation,”, but Fidesz said that it would only meet with Laszlo Solvom, Hungary’s president.
Its smaller ally, the Christian Democratic People’s Party, also said it would not attend.
Hungary has seen its worst street violence since the fall of communism at the end of the 1980s after Gyurcsany was caught on tape telling his Socialist party that they “did nothing for four years” and lied to win re-election.
Gyurcsany has said he is seeking to shock his party into backing reforms and has defied opposition calls to quit.
“This [rally] will be a watershed”
Viktor Orban, the Fidesz leader
Fidesz has called a rally for Saturday, which could draw hundreds of thousands of people, to protest against the government.
The government wants the rally to be cancelled.
There are fears that the rally could turn violent if far-right groups attach themselves to it.
The Fidesz leader, Viktor Orban, told the Heti Valasz weekly that the rally was to be held on Heroes Square, where he spoke in 1989 at the re-burial of Imre Nagy, the prime minister executed by the Russians for leading the 1956 uprising against Soviet rule.
“This [rally] will be a watershed,” Orban said.
Wednesday night’s protests were largely peaceful, although Pal Gyorfi, National Ambulance spokesman, told news agency MTI that 16 people had been taken to hospital with injuries.
That was far lower than the over 200 injured on previous nights.