Originally Published: 11 APR 23 10:55 ET

Updated: 11 APR 23 11:03 ET

By Casey Gannon and Katelyn Polantz, CNN

(CNN) -- Donald Trump's close presidential aide and speechwriter Stephen Miller returned to testify to a federal grand jury in Washington on Tuesday after the courts ordered that he and other top advisers must share their recollections of direct conversations with the then-president related to the January 6, 2021, Capitol riot.

Miller is likely to be asked in the grand jury about his phone call with Trump minutes before the Ellipse rally that day, and other conversations they had about the election. The grand jury is hearing evidence as part of a special counsel's criminal investigation.

Miller's appearance at the federal courthouse Tuesday morning -- alongside his lawyer and prosecutors from the office of special counsel Jack Smith -- adds to a parade of witnesses the 2020 election investigators have secured in recent weeks.

Miller and his attorney declined to comment Tuesday.

Late last month, the chief judge overseeing the grand jury denied Trump's attempts to protect his presidential communications from investigators, prompting witnesses like Miller, who previously avoided answering some questions, to testify again.

Miller previously appeared before the grand jury in November. At that time, CNN reported that he declined to answer some questions because of Trump's wish to assert executive privilege and protect the secrecy of some of their conversations during his presidency.

In his separate interview with House January 6 investigators, Miller declined to share details about conversations with Trump related to the then-president's unwillingness to concede the election if he lost and the discussions they had about speeches Miller prepared after the election, according to a publicly available transcript.

The House investigation found that after the call between Miller and Trump the morning of January 6, Miller added in "POTUS edits" to Trump's Ellipse speech that included a mention of then-Vice President Mike Pence having the ability to overturn the election result -- a power Pence himself believed he didn't have.

"We will see whether Mike Pence enters history as a truly great and courageous leader. All he has to do is refer the illegally-submitted electoral votes back to the states," the draft read. Another White House adviser then asked Miller to remove the Pence reference from the speech's text. Pence and Trump then had an angry phone call, and the speechwriting team reinserted a line about Pence.

Criminal investigators from the special counsel's office have been pursuing questions about Trump's pressure campaign on Pence, and they're securing testimony about it from a number of witnesses in recent weeks. Pence himself could testify as soon as this week.

The grand jury proceedings are secret, and the special counsel's office hasn't filed any charges.