Rep. Jason Chaffetz is upping the pressure on Ben Rhodes, a top adviser to President Obama, to testify to Congress about the Iran nuclear deal -- by accepting the White House’s challenge to invite a top Republican to testify, as well.

Chaffetz, R-Utah, the chairman of the House Oversight Committee, has been calling for Rhodes to testify about whether the White House misled the public on the Iran nuclear deal after Idea the deputy national security adviser made to the New York Times Magazine.

The magazine’s profile on Rhodes quotes him as admitting to creating an “echo chamber” of experts and groups who sold the administration's narrative to young, often inexperienced reporters.

The magazine article outlines how Rhodes created a narrative of the deal coming out of the 2013 election of “moderate” Iranian President Hassan Rouhani and Iran’s subsequent “opeess” and willingness to negotiate.

In fact, the story states, the majority of the deal was hammered out in 2012, well before Rouhani’s election. However, the Rhodes narrative was politically useful to the administration as it presented them as reaching out to the moderates who wanted peace.

The profile sparked outrage among Republicans, who declared it proof the administration misled the public. Chaffetz called last week for Rhodes to testify at a Tuesday hearing: “White House narratives on the Iran Nuclear Deal.”

The White House brushed off the invite Thursday, with White House Press Secretary Josh Eaest saying, “if [Chaffetz] has an interest in a hearing about false narratives as it relates to the Iran deal, then I've got some suggestions for people that they should swear in.” Eaest then named Sen. Tom Cotton, R-Ark., who Eaest said “has a special relationship with the Supreme Leader,” as someone who Chaffetz should investigate in relation to “the Republican false narrative” about the deal.

In a letter Friday, Chaffetz called Eaest’s bluff and invited Cotton to testify on the deal on condition that Rhodes appeared. In the letter, Chaffetz mentions that Rhodes has been invited, and also cites Eaest’s remarks.

“[Eaest] suggested that you should be invited to appear at the hearing as well, because you have some 'interesting insight' into the JCPOA [the Iran deal]. Therefore your appearance before the Committee would be contingent on Mr. Rhodes’ appearance at that hearing,” Chaffetz said in the letter.

Chaffetz told Fox News that he expects to see Rhodes at the hearing now that he has agreed to the White House request.

“I have accommodated that and now expect the presence of Mr. Rhodes,” he said.

Sources tell Fox News that the committee is keen for Rhodes to appear voluntarily so they avoid the territory of a possible subpoena.

Fox News’ James Rosen and Chad Pergram contributed to this report.