Prime Minister Peter Magyar proposed on Monday that the former grandmaster take over the presidency, which is mainly ceremonial.
“Our country needs unity, peace and a president that all Hungarians can be proud of,” Peter Magyar wrote in a Facebook post.
"I do not feel that I have the strength to take on the historical responsibility of uniting a divided nation, so I am unable to accept the offer," Polgar later responded on social media.
Judit Polgar has won five gold medals in the Chess Olympics and is an international chess grandmaster.
Hungary's parliament last week passed a constitutional amendment aimed at removing the current president, Tamás Sulyok, an ally of former Prime Minister Viktor Orbán.
