Petersen, a graduate of the University of Virginia Law School, has been a member of the Federal Election Commission since 2008.
A White House official says Petersen has withdrawn his nomination and that Trump has accepted the withdrawal.
Summary: Another one of President Trump's judicial nominees withdraws from being considered after it became clear his qualifications were not up to par.
The two other nominees who were pressured to bow out of the running were Brett Talley, who was found to have a conflict of interest because his wife works in the Trump White House, not to mention his lack of experience, and Jeff Mateer, who had a history of making some controversial comments. Starting with his nomination of Supreme Court Justice Neil Gorsuch in January, the president has chosen deeply conservative, often outspoken judges, lawyers, professors and bloggers to fill seats that Republicans left vacant under Barack Obama.
During Wednesday's (US time) confirmation hearing, Kennedy started by asking Petersen and four other nominees who appeared with him, "Have any of you not tried a case to verdict in a courtroom?"
PETERSEN: Yes. I haven't, I'm, again, my background is not in litigation as when I was replying to Chairman (Chuck) Grassley (R-Iowa), I haven't had to um, again, do a deep dive.
The statement ignored the fact that Kennedy, a Republican whom backed Trump during his campaign, was the senator who led the charge against Petersen.More news: Foodpanda is Ola's chef in battle with Uber
More news: NBC In Early Talks to Revive The Office
More news: 'Thousands' of emails uncovered in Trump Russia probe
Senator Kennedy: Have you ever taken a deposition by yourself?
Kennedy said Monday that "I feel bad for [Petersen], but I think he did the right thing, stepping - standing aside".
Because if anyone knows about qualifications, it's President Trump.
When asked, Kennedy would not criticise the White House vetting process, claiming that he has "no idea" how they make their selections and that "the track record of the White House is pretty good" when it comes to selecting and confirming judicial nominees. John Kennedy of Louisiana quickly went viral.
Kennedy said that Trump was not upset with him during their conversation.
The episode caused the senator to receive a great deal of media attention, and he was recently quoted saying "just because you've seen My Cousin Vinny doesn't qualify you to be a federal judge. I would strongly suggest he not give up his day job". Can you tell me what the Daubert standard is?
He said that the judgeship he was up for - a judge on the federal district court for the District of Columbia - where his experience with administrative and constitutional law would tie in perfectly with the cases of regulatory matters and challenges to agency actions dominate the docket.
Kennedy said that Trump called him Saturday to talk about the nominee.