Michael Cohen, President Donald Trump's former personal lawyer, has continued to give special counsel Robert Mueller helpful information for his probe into Russian interference in the 2016 election, according to a new filing Friday.

Mueller specifically said that Cohen, in interviews with the special counsel's office, has given "relevant and useful information" about contacts with people connected to the White House from 2017 until this year.

Cohen also gave Mueller's team "useful information concerning certain discrete Russia-related matters core to" Mueller's investigation that he "obtained by virtue of his regular contact with [Trump Organization] executives during the" 2016 presidential campaign.

And Cohen gave Mueller "information about attempts by other Russian nationals to reach" Trump's presidential campaign as far back as November 2015.

Cohen made "substantial and significant efforts to remediate his misconduct," and to help Mueller's ongoing criminal investigations, according to the filing.

Mueller is investigating Russian efforts to influence the 2016 election and possible collusion in those attempts by members of Trump's campaign.

In a court document, Mueller also said he was not taking a position on what sentence Cohen should receive next Wednesday when he is sentenced for the crime of lying to Congress, which is the only charge to have been lodged against the lawyer by the special counsel.

Cohen is also due to be sentenced that same day for financial crimes and campaign violations lodged by federal prosecutors in New York, who have asked for a "substantial" term of imprisonment.

But any sentence for lying to Congress that Cohen gets should be served concurrently with the punishment imposed for the other crimes, Mueller's office wrote in the sentencing memo filed in U.S. District Court in Manhattan.

"Cohen has taken responsibility for his wrongdoing and is willing to face the consequences," Mueller's office said.

The 52-year-old Cohen last week pleaded guilty to the crime of misleading Congress.

He had understated the level of involvement and awareness Trump had in a ultimately aborted deal to build a Trump Tower in Moscow.

Cohen also had lied by falsely claiming to Congress that the project died in January 2016, when it actually was still being pursued months later, when Trump had become the presumptive Republican Party nominee for president.

Cohen did so, according to Mueller, "in hopes of limiting the ongoing Russia investigations being conducted by Congress" and the special counsel.