Former President Trump has arrived at the courthouse for today's proceedings.

This will be the final day of court this week, as court is off on Friday for Trump to attend his son Barron's high school graduation.

Michael Cohen has arrived at the lower Manhattan courthouse for his testimony this morning.

Proceedings are scheduled to get underway at 9:30 a.m. ET.

Testimony is scheduled to conclude at 4 p.m., after which Judge Juan Merchan is scheduled to hear arguments from the parties about the bounds of potential testimony from a defense expert witness.

Michael Cohen returns to the witness stand this morning, where the former Trump attorney is expected to face a full day of cross-examination.

Cohen, under direct examination earlier this week, described in-person meetings and phone calls with Donald Trump, who he said joined into an agreement with tabloid publisher David Pecker to catch and kill negative stories ahead of the 2016 election; approved a $130,000 hush money payment from Cohen to Stormy Daniels; and signed off on an arrangement to reimburse Cohen in 2017 using what prosecutors say were falsified invoices. Trump has denied all wrongdoing.

Defense attorneys are expected to question Cohen's credibility based on his past testimony and previous statements he has made in interviews, podcast and books.

Former President Trump has asked New York's highest court to rescind the limited gag order that prevents him from commenting publicly about witnesses, jurors and lawyers in his ongoing criminal trial, according to a new court filing.

The filing is sealed, but is the next step after an intermediate appeals court yesterday upheld the order imposed by trial Judge Juan Merchan.

Trump has frequently attacked the judge, which is permitted, and has called the limited gag order unconstitutional.

In its ruling yesterday, the intermediate appellate court said that Merchan had appropriately balanced Trump's free speech rights with the court's need to control the trial.

There was no immediate comment from the Manhattan DA's office.

-ABC News' Katherine Faulders contributed to this report

After Cohen's recording was played in court, prosecutor Susan Hoffinger is replayed sections and asked Cohen about what he said at the time.

"Who is 'our friend David?'" Hoffinger asked.

"He is referring to David Pecker," Cohen said.

Asked about the reference to then-Trump Organization CFO Allen Weisselberg, Cohen said, "Because Mr. Trump had previously directed me to speak with Allen Weisselberg about getting this matter settled."

"Because we are going to need money and going to need to open the LLC and to resolve this issue," Cohen said about the LLC being formed.

"We were referring to the 150,000 that was advanced by AMI in order to purchase the life rights of Karen McDougal," Cohen said "He knew already knew based on conversations with David which is why he mentioned the number 150."

When asked about the comment about Pecker getting "hit by a truck," Cohen said that Trump was concerned about the National Enquirer's files about him in case Pecker ever left the company.

"David Pecker was being considered for the CEO position of Time Inc. and the concern was the information -- so all the stuff refers to that," Cohen said

Following this testimony, court was recessed for the mid-morning break.

Cohen, exiting the courtroom, did not appear to look at Trump as he walked by the defense counsel table.