Ponta refused, saying that only Parliament could dismiss him.
President Klaus Iohannis said after meeting Ponta that it was "an impossible situation for Romania for the prime minister to be accused of criminal acts." Iohannis warned that Romania could be embroiled in a political crisis if he did not resign.
The 42-year-old premier had met earlier with the anti-corruption prosecutor's office and then told reporters he was suspected met of making false statements, money laundering and being an accomplice to tax evasion. He had not previously been identified as a suspect in the anti-corruption drive.
The allegations relate to his work as a lawyer from 2007 to 2008 when he was also a lawmaker for the Social Democratic Party.
Ponta is the most prominent suspect to be identified as Romania's anti-corruption drive has intensified in recent months.