Fiala told parliament he would discuss the possibility in his ruling coalition, after Hamas militants carried out the deadliest attack on civilians in Israeli history on Saturday.
"I believe the situation now is such that we should speed it up to unequivocally support Israel," Fiala said when asked about a potential move.
"It is an issue that can be resolved in a matter of months, not years and not weeks," he said, just days after his foreign minister warned against such a move, saying it would be illegal and also risky at such a time.
The Czech Republic opened a diplomatic office in Jerusalem in 2021, a step that drew protests from the Palestinian Authority and the Arab League.
Fiala, leader of the centre-right Civic Democrats, said the decision would have to be carefully prepared to avoid surprising partners, and security issues needed to be addressed.
Israel's government regards Jerusalem as the eternal and indivisible capital of the country, although that is not recognised internationally.
Palestinians want East Jerusalem - which Israel captured in the 1967 Middle East war and later annexed in a move not recognised internationally - as the capital of a future Palestinian state.
The Czech Republic, a long-time supporter of Israel, would be the second NATO country to move its embassy to Jerusalem after the United States, which did so in 2018 under the Trump administration. It would be the first European Union state to move its embassy.
"I do not think we would have to proceed in consensus with all EU countries, we never had that in the case of Israel," Fiala said.
However, Foreign Minister Jan Lipavsky from the liberal Pirate Party -- who became the first foreign minister on Tuesday to visit Israel to demonstrate solidarity -- said this week that conditions were not in place for moving the embassy.
He said it would go against international law and United Nations Security Council resolutions, undermine European unity when it is needed in the face of Russia's aggression in Ukraine, and pose a security threat to Czech diplomatic missions.
President Petr Pavel has also said it was not the time for debate on an embassy move while Israel was fighting a war.
(Reporting by Jan Lopatka; Editing by Gareth Jones)
