The government said it would invite the amended bids from South Korea's KHNP and France's EDF by April 15. Another bidder for the tender, U.S. group Westinghouse (WAB.N), opens new tab, did not meet conditions.
Seeking bids for more units will help push prices per block by up to a quarter if four were built, government officials said.
"Based on (the bids), we will then select a supplier and decide whether we will have more reactors built or not," Prime Minister Petr Fiala said at a press conference.
The Czech Republic has long sought more nuclear power capacity as it needs to replace ageing units in the coming decades and cover rising consumption while shutting coal-fired plants and facing limits to renewable power.
Majority state-owned utility CEZ (CEZP.PR), opens new tab has been running the tender for the multi-billion dollar project to build one new unit at its Dukovany nuclear power plant and had sought only indicative offers for more units.
CEZ has agreed a financing model with the government for the construction of the new Dukovany unit - which remains in place - but management has said the company could not replicate the model four times.
Finance Minister Zbynek Stanjura said on Wednesday an expert group would draft financing models for any further blocks, without giving details what it would mean for CEZ.
The government has been looking at ways to restructure CEZ, possibly taking larger control of its production unit, as it considers ways to finance a bigger nuclear buildup. Fiala also said following Russia's invasion of Ukraine in 2022 that the state needed control of power production.
CEZ is one of central Europe's biggest companies and has a market capitalisation of $21 billion. Its shares are around one-year lows, and down 1% on Wednesday, and have been held back by uncertainty over its future structure.
The government expects a decision on the nuclear supplier in June. With the binding option for three additional units in place, a decision on the number of units may be taken later.
Industry Minister Jozef Sikela said it may be reasonable to build two units in one location together or in succession, which would mean two at Dukovany and possibly two later at CEZ's Temelin nuclear power plant.
The project's timetable aims to bring the first unit online in 2036.
