The daily O Globo published its call in an editorial Friday afternoon shortly after Brazil's supreme court revealed several accusations against Temer made by a business mogul.
JBS company owner Joesley Batista said he paid bribes to Temer from 2010 to this year, among other accusations. Attorney General Rodrigo Janot has accused the president of corruption.
O Globo has backed Temer's pledge for austerity measures and reforms, but now says the president lacks the moral, ethical, political and administrative tools to remain.
Temer has denied any wrongdoing and on Thursday he promised not to resign.
Batista also said that he transferred $150 million to offshore accounts for campaigns of former Brazilian Presidents Luiz Inacio Lula da Silva and Dilma Rousseff.
In a plea bargain testimony released Friday, Batista said that former Finance Minister Guido Mantega was the middleman in the operation to channel illegal funds for Silva and Rousseff.
Batista said both former presidents were aware of the transfers, but did not name where those accounts were based. Batista also didn't state for which campaigns the money was transferred.
Rousseff denied the accusations in a statement and said she never had offshore bank accounts. Silva's spokesman said Batista's accusations are hearsay that was never investigated.