The tabloid publisher has agreed to continue co-operating with investigators.
On Wednesday, Cohen was sentenced to 36 months in prison, and took several hard shots at Trump while he was in court to receive that sentence. And if it was a prohibited contribution, Trump said, Cohen is the one who should be held responsible.
Scannell, who was inside the courtroom, said Cohen teared up as he spoke to the judge about bringing pain and shame to his family.
Cohen's lawyers had argued for leniency, saying he made a decision to cooperate with investigators rather than hold out for a possible pardon.
Trump claimed that USA tariffs on Chinese imports generated $11 billion in the last four months, which appears to be a significant exaggeration.
Mr Trump claimed that because he acted on "advice of counsel", he is off the hook for any crime.
He said Cohen "probably was not guilty" of those campaign violations but pleaded guilty to benefit himself.
The president denies the affair. However, the sentence still stressed the seriousness of violating campaign finance laws and seeking to influence the outcome of an election.
Cohen, wearing a dark suit with a light blue tie, arrived for the sentencing with his wife, son and daughter, who was walking with a crutch.
"He has provided consistent and credible information about core Russia-related issues under investigation", she said without elaborating.
'Because what that means is, this is not simply Michael Cohen's word against Donald Trump's, it is now Donald Trump's word against everyone else, ' he added. If Trump wins reelection, when he leaves office the statute would have expired on any campaign finance violations from his 2016 election.More news: China slams ‘inhumane’ treatment of Huawei executive, says Canada violates her rights
Cohen told prosecutors that the $130,000 payment to Daniels and the $150,000 payment to McDougal were at the direction of Trump, implicating the president in a possible violation of campaign finance law.
Michael Cohen leaves Federal court, in New York, August 21, 2018.
"It was my duty to cover up his dirty deeds", Cohen said as he pleaded for leniency before US District Judge William H. Pauley III.
Why Trump is likely to be indicted by Manhattan US Attorney.
He called for a sentence that sends a message that "even powerful, privileged individuals can not violate these laws with impunity". That position contradicts federal prosecutors, who said in court Wednesday that Cohen paid hush money to "two women who threatened to go public with details of purported extramarital affairs, and Mr. Cohen admitted that he did so in coordination with and at the direction of Individual One", that is, Mr. Trump.
He had told prosecutors during his guilty plea that Trump had directed him to make the hush money payments.
Before the sentencing, he called for Cohen to serve a full sentence in prison.
President Donald Trump has insisted he "never directed" his former lawyer Michael Cohen to break the law.
Cohen is due to begin his sentence on March 6.
But legal analysts said the accusations against Trump could amount to a felony because they revolve around an alleged conspiracy to hide payments from campaign contribution reports - and from voters. The National Enquirer's parent company was chaired at the time by Trump's longtime confidante, David Pecker.
Trump has offered a shifting defence on the payments to the women, first saying in April that he did not know about the payments to later appearing to acknowledge they were made but saying they were unrelated to campaign finances.