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

According to a transcript of the day's court proceedings released this evening, Donald Trump and his attorneys have not yet decided if the former president will testify at his trial.

The transcript included a private sidebar conference held this morning, during which Judge Juan Merchan asked defense lawyers about Trump's possible testimony.

"And do you have any indication whether your client is going to testify?" Merchan asked defense attorney Todd Blanche.

"No," Blanche replied.

"No determination yet?" Merchan asked.

"No," Blanche said.

The conversation happened outside of the earshot of reporters and members of the jury.

Speaking to reporters after exiting the courtroom, former President Trump was asked about today's testimony, as well as if he plans to testify during the trial.

"As you know, I'm under a gag order. So I can't really answer those very simple questions that you're asking," Trump said, referring to the order that prohibits him from making public comments about jurors, witnesses and lawyers in the case, but does not keep him from discussing the case itself.

"We'd love to not be in the gag order. I'm the Republican nominee for president. I'm leading in every poll, and I have a gag order."

Recapping his day in court, Trump said, "We had a very, I think, a very good day and important to see what's happening and you'll have to record it because I can't talk about it too much."

"We had a very good day. I think we're exposing the scam for what it is," he said.

-ABC News' Kelsey Walsh and Mike Pappano

Michael Cohen, his testimony done for the day, left the courtroom without looking at Trump.

During a bench conference, defense attorney Todd Blanche said he wants to explore with the court and the opposing counsel the admissibility of a defense expert witness before deciding whether to call him.

The judge set a conference to take place Thursday at 4 p.m. ET, after the jury is excused slightly early for the day.

Asked about Thursday's timing for the remainder of his cross-examination of Cohen, Blanche told the judge, "If I finish, it's at the end of the day."

The rest of the parties then departed the courtroom.

Michael Cohen told jurors that he submitted 11 invoices to the Trump Organization over the course of 2017 to get his reimbursement for the Stormy Daniels hush money payment and other expenses -- but that they were false records because they were not for their stated purpose of a retainer fee.

Asked the purpose of the $420,000 payment over the year, Cohen said "the reimbursement to me of the hush money fee along with Red Finch, and the bonus."

"Was this invoice a false record?" prosecutor Susan Hoffinger asked.

"Yes ma'am," Cohen said.

"Were any of those invoices you submitted for services performed pursuant to a retainer agreement?" Hoffinger asked.

"No," Cohen replied.

Hoffinger then walked Cohen through each of the false invoices he sent, and the checks that he received in return.

As Hoffinger showed Cohen each document, he confirmed that there was no retainer agreement at the time and that the invoices were false.

"Is that a false record?" Hoffinger asked about each invoice.

"Yes ma'am," Cohen said.

After each invoice, Cohen identified the check he received.

"Did you receive this check for $35,000 in response to that false invoice?" Hoffinger asked.

"Yes ma'am," Cohen replied.

"Whose signature is it?" asked Hoffinger.

"Donald J. Trump" said Cohen.

"Was this the last check that you received from Mr. Trump or anyone at the Trump Organization?" Hoffinger asked about a December 2017 check for $35,000.

"Yes," Cohen said, explaining that the "full reimbursement of the $420,0000 had been paid."