PRAGUE, June 28 (Reuters) - The Czech government does not want to introduce a tax on windfall profits at energy firms but wants to explore what form of solidarity those firms can provide to the rest of the society, Prime Minister Petr Fiala said on Tuesday.

Czech energy companies, including 70% state-owned electricity producer CEZ, have seen their profits rising in the past months on the back of soaring energy prices, which in turn put pressure on consumers and companies.

Shares in CEZ slumped by 10.9% on Monday after a television report on the junior ruling Pirate party proposing several options for a windfall tax on energy firms and most other ruling parties backing a debate.

"We do not want to introduce a sector tax as such... but what serious debate should be led on is that as a result of the situation in world markets, profits of energy firms grew significantly," Fiala told a briefing shown live on television.

"In this constellation, it is really proper to consider which form to choose to show solidarity of those who have these profits toward those who are heavily affected by the situation."

On Tuesday, CEZ recovered some of the losses, as it widened its gains to 4.4% from 2.6% before Fiala's comments reiterating his opposition to a special tax as such.

"They are moving cautiously as introducing a new tax could be tough," said Milan Vanicek, chief analyst at J&T Banka.

"I can imagine other ways, like higher dividend from CEZ or some social tariffs," he said. Fiala did not give any details on other possible forms of "solidarity".

The Sev.en group of Pavel Tykac or Daniel Kretinsky's EPH are other major electricity producers in the country.

CEZ was holding an annual shareholders meeting on Tuesday which was due to vote on the management's proposal for a 44 crown per share dividend and a government counter-proposal for a 48-crown payout, sweetened by a delay in payment until November to give CEZ a buffer to preserve cash. The government's proposal was expected to win given the government controls 70% stake.

(Reporting by Jan Lopatka and Robert Muller, Editing by William Maclean)