Cohen had previously said that talks on the Moscow project had ended in January 2016, just before the Iowa caucuses.
Cohen's revelations are potentially significant, as they seem to show that Trump was engaged in commercial relations with Russia in the midst of a campaign in which Moscow intervened to help in his election.
This could also intersect other information that Mueller knows to create a political and legal risk for the president.
Cohen waived his right to an indictment when he appeared in federal court in New York.
"In truth and in fact, and as Cohen was well aware, Cohen's statements regarding the Moscow project that he presented to the House and Senate intelligence committees were false and misleading," the office said. Mueller in a folder.
"Cohen made false statements to … give the false impression that the Moscow project ended before" the Iowa caucus and … the very first primary ", in the hope of limit current investigations on Russia, "the document added.
"It's a weak person," Trump said before leaving for Buenos Aires, Argentina.
"He was sentenced to quite a long time with things unrelated to the Trump organization," Trump said, citing Cohen's legal issues regarding mortgages and the IRS.
"What he's trying to do, is to get a reduced sentence," Trump said.
Cohen's charge is punishable by up to five years' imprisonment, a fine of up to $ 250,000, and maximum supervision of up to three years. The penalty has been set for 12 December.
Cohen left the courthouse without making a statement.
This story begins and will be updated.
Betsy Klein and Julia Jones of CNN contributed to this report.