Trump, in turn, called Cohen a "weak person" who is lying to get a lighter sentence.
Flanked by his lawyers, Cohen admitted making false statements about the project in 2017 to Senate and House intelligence committees, which at the time were investigating possible connections between the Trump campaign and Russia.
Cohen told the judge he lied about the timing of the negotiations and other details to be consistent with Trump's "political message." Cohen and prosecutors referred to Trump as "individual one" throughout Thursday's proceedings and said he lied "to be loyal to Individual One."
Among other lies, Cohen said he told Congress that all discussions about building a Trump Tower in Moscow had ended by January 2016, when they had actually continued until June of that year. He said he also lied about his contacts with Russian officials and lied when he said he never agreed to travel to Russia in connection with the project and never considered asking Trump to travel to support the project.
Prosecutors said in a court complaint that Cohen had misled Congress to give a false impression that the Moscow project had ended before the Iowa caucus and first Republican presidential primary in 2016.
As he left the White House shortly after the court proceeding concluded, Trump called Cohen "a weak person"
"Michael Cohen is lying and he's trying to get a reduced sentence," Trump said.
Nothing said in court, or in associated court filings, addressed whether Trump or his aides had directed Cohen to mislead Congress.
The charges were brought by Special Counsel Robert Mueller, who is investigating Russian interference in the presidential election, not the prosecutors in New York who handled Cohen's previous guilty plea in August to other federal charges involving his taxi businesses, bank fraud and his campaign work for Trump
Cohen's lawyer, Guy Petrillo, said he would give the court a letter outlining how his client has cooperated with Mueller's investigation.
Cohen declined to comment as he left the courthouse.
Reacting to the plea to the new charges, House Speaker Paul Ryan said Cohen "should be prosecuted to the extent of the law. That's why we put people under oath."
Cohen gave a statement to congressional committees last year saying the president's company pursued a project in Moscow during the Republican primary but that the plan was abandoned "for a variety of business reasons."
Cohen also said he sent an email to the spokesman for Russian President Vladimir Putin as part of the potential deal.
In his statement, he said that he worked on the real estate proposal with Felix Sater, a Russia-born associate who he said claimed to have deep connections in Moscow.
The discussions about the potential development began after Trump had declared his candidacy. Cohen had said the talks ended when he determined that the project was not feasible.
Cohen had also disclosed that Trump was personally aware of the deal, signing a letter of intent and discussing it with Cohen on two other occasions.
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