Federal lawmakers attributed Bannon's silence Tuesday before the House intelligence committee to the White House - saying officials told him to refuse to discuss his time in President Donald Trump's administration or his transition team.
According to Axios, Bannon realized immediately after divulging details about his conversations with then-White House press secretary Sean Spicer, then-chief of staff Reince Priebus, and Trump legal team spokesman Mark Corallo that he had made a mistake, because they occurred while Bannon was serving as chief strategist in the White House.
Mr Bannon was sacked by the White House in August previous year, and he returned to the right-wing news website Breitbart News.
The subpoena is a sign that Bannon is not personally the focus of the investigation.
In reporter Michael Wolff's exposé Fire and Fury, Bannon is quoted at-length calling the meeting "treasonous" and "unpatriotic". "Clearly Mr. Bannon's being treated differently; differently by the White House and differently by the majority", Schiff said.
A spokeswoman for Bannon did not respond to multiple requests for comment.
GOP Rep. Trey Gowdy of SC and Democratic Rep. Adam Schiff of California used Bannon's "slip-up" to try to press him into answering other questions about his time at the White House, the report said.
"This was effectively a gag order by the White House preventing this witness from answering nearly any question concerning his time in the administration and many questions even after he left the administration", Mr Schiff said.
The White House on Wednesday refused to say whether it had actually invoked executive privilege, however. "Sometimes they have a White House attorney present in the room".
"I think he will remain fit for duty for the remainder of this term and even the remainder of another term if he is elected", Jackson said. "Now, as a committee, if we follow the practice that we maintained yesterday, we should have subpoenaed him today and compelled answers to those questions".
Mueller's issuance of a grand jury subpoena indicates he does not consider Bannon to be a target of the probe, since targets are subpoenaed in front of a grand jury only in rare circumstances.
The subpoena was issued last week, according to a person familiar with the situation, who said that Bannon expects to be able to persuade the special counsel's office to accept a voluntary interview of Bannon by prosecutors in place of a grand jury appearance.
"Donald Trump entered office with the most blatant and potentially corrupting conflicts of interest in the history of American politics and things only got worse from there", said Robert Weissman, president of Public Citizen, a liberal-leaning nonprofit based in Washington.