U.S. President Donald Trump ordered Michael Cohen, his personal lawyer, to make illegal hush payments to two women ahead of the 2016 presidential election in a blatant violation of federal election laws, said federal prosecutors in separate court filings in New York.

The filings on Dec. 7 were the first time federal prosecutors officially agreed that Cohen made the payments to two women -- porn actress Stormy Daniels and former Playboy model Karen McDougal -- in "coordination with and under the direction of" Trump.

Cohen made the same assertion when he implicated Trump in the hush money payments in his guilty plea in August in New York.

The documents, however, do not answer the core question at the heart of Special Counsel Robert Mueller's probe into Russian election interference abetted by the Trump campaign -- did the president or those around him conspire with the Russia to rig the election.

Federal prosecutors in New York and those working for Mueller made the case for why Cohen and former Trump campaign chairman, Paul Manafort, both deserve to be jailed for their crimes.

In total, the prosecutors seem to be saying Trump was more aware that he has claimed to be about the hush money payments to these two women, said federal prosecutor Michael Zeldin.

The documents added more legal pressure on Trump by confirming prosecutors' belief of his involvement in a campaign finance violation.

Prosecutors in both of the Cohen cases were required to submit separate memos on Cohen's cooperation to U.S. District Judge William Pauley in Manhattan. Pauley will decide Cohen's sentence on Dec. 12.

Prosecutors argue Trump as being directly involved in efforts to buy the silence of women who might go public in allegations against him.

The memo from New York prosecutors identifies three men at a meeting in August 2014: Cohen, "Individual 1" and "Chairman 1." Individual 1 is Trump and Chairman 1 is David Pecker of the National Enquirer.

The filing says that Chairman-1 (Pecker) met with Cohen and Individual-1 (Trump). Pecker offered to help deal with negative stories about Trump's relationships with women by identifying these stories so that they could be purchased and "killed," or not published.

In August Cohen pled guilty to violating campaign finance law when he arranged payments to Stormy Daniels during the 2016 presidential election. He also pled guilty to other crimes, including making a false statement to a bank. Recently, he pled guilty to lying to Congress about efforts during the presidential campaign to build a Trump-branded tower in Moscow.

The Democratic Party, which won control of the House of Representatives in the midterm election of Nov. 6, praised the conclusions, and called for steps to protect Mueller's probe from being terminated by Trump.

Sen. Diane Feinstein (D-CA) said these legal documents "outline serious and criminal wrongdoing, including felony violations of campaign finance laws at the direction of President Trump."

Trump has repeatedly denied any collusion with Russia. In reaction to the court filings, Trump tweeted he was vindicated. "Totally clears the president. Thank you!"