The White House did not immediately return a request for comment. Press secretary Sarah Sanders said on Friday that Cohen has lied repeatedly and that the filing was insignificant.
U.S. President Donald Trump could face impeachment and jail time if hush money payments reported by his former lawyer are proven to be campaign finance violations, Democratic lawmakers said on Sunday.
Court filings on Friday in cases that stemmed from a federal probe into Russian activities during the 2016 presidential election pointed to potential problem areas for Trump, including whether he instructed six-figure payments to two women during the campaign to keep quiet about affairs.
Federal prosecutors sought prison time for longtime Trump "fixer" Michael Cohen for paying off an adult film star and a former Playboy model at Trump's behest, evading taxes and lying to Congress about a proposed Trump Organization building in Moscow.
If the payments are proven to be felony campaign finance violations, Democratic U.S. Representative Jerrold Nadler told CNN those would be grounds for impeachment.
"Well, they would be impeachable offenses. Whether they are important enough to justify an impeachment is a different question," said Nadler, who will lead the Judiciary Committee when Democrats take control of the House of Representatives in January.
Under U.S. law, campaign contributions, defined as things of value given to a campaign to influence an election, must be disclosed. Such payments are also limited to US$2,700 per person.
Friday's court filings also revealed new information about contacts between people working for Trump and Russians in the cases of Cohen, Trump's former longtime personal lawyer, and Paul Manafort, Trump's short-lived campaign chairman who was convicted in August on tax and bank fraud charges.
Special Counsel Robert Mueller said Manafort lied to investigators about his interactions with a Russian tied to Russian intelligence services. Mueller's office said the lying prompted prosecutors last week to retract a plea agreement with Manafort on two separate conspiracy charges.
"I think what these indictments and filings show is that the president was at the center of a massive fraud - several massive frauds — against the American people," Nadler told CNN.
Mueller is investigating Russian interference in the 2016 presidential election and whether Trump's campaign colluded with Moscow to sway the election. Russia denies interfering in the 2016 election and Trump has denied any collusion occurred.
The investigation has cast a shadow over Trump's presidency, with its implication Moscow may have had a hand in his White House victory. The Republican president repeatedly has expressed his impatience with the probe that Mueller took over in March 2017, saying it was politically motivated.
Trump said the filings did not prove any collusion with Russia and called for an end to the investigation. "Time for the Witch Hunt to END!" Trump said in a Twitter post on Saturday.
However, the end of the Mueller probe could be the beginning of bigger problems for Trump. "There's a very real prospect that on the day Donald Trump leaves office the Justice Department may indict him, that he may be the first president in quite some time to face the real prospect of jail time," Representative Adam Schiff, the Democrat who will lead the House Intelligence Committee next year, told CBS' "Face the Nation."
Legal experts are divided over whether a sitting president can be charged with a crime, as well as on whether a violation of campaign finance law would be an impeachable offense.
Republican Senator Rand Paul warned against over-criminalizing campaign finance violations, telling NBC's "Meet the Press" that errors in disclosures should be punished with fines, not jail.
Republican Senator Marco Rubio told CNN he was waiting for the results of the Russia investigation and related federal probes. However, he cautioned that "no one should be above the law."
Rubio said it would be a "terrible mistake" if Trump pardoned Manafort, saying that "could trigger a debate about whether the pardon powers should be amended." Trump has not ruled out a pardon for Manafort, praising him as a good man. In contrast, he has said Cohen, who has cooperated with federal prosecutors, should go to jail.
Schiff said Trump may end up needing to seek a pardon for himself from the next U.S. president. House Democrats have promised an array of investigations into Trump's activities. "What is clear also is that the Republican Congress absolutely tried to shield the president," Nadler said. "The new Congress will not try to shield the president."