Mitt Romney said Tuesday that reports claiming he does not think a Muslim would be needed in his Cabinet are inaccurate, and that he would consider applicants "of any faith and ethnic group" for positions in a Romney administration.

"The people who would be part of my Cabinet is something that I really haven’t given a lot of thought to at this point," Romney said, speaking to reporters at a campaign stop in St. Petersburg, Fla. "But I don’t have boxes I check off as to their ethnicity."

Romney was responding to a critical opinion piece in Tuesday's Christian Science Monitor by Muslim businessman Mansoor Ijaz.

Ijaz wrote that during an exchange with the GOP candidate, he asked Romney whether he would consider including Muslims in his Cabinet as advisers on national security matters. Ijaz claimed Romney told him "based on the numbers of American Muslims ... in our population, I cannot see that a Cabinet position would be justified. But of course, I would imagine that Muslims could serve at lower levels of my administration."

Click here to read the opinion piece.

Politico.com later reported that Romney claimed Muslims are not needed in his Cabinet.

Romney disputed Ijaz's account of the conversation on Tuesday.

"That's not ... his question was, 'Did I need to have a Muslim in my Cabinet to be able to confront radical jihad and would it be important to have a Muslim in my Cabinet?' And I said, 'No, I don’t think that you have to have a Muslim in the Cabinet to be able to, to take on radical jihad any more than in the second World War where you needed to have a Japanese American to help us understand the threat that was coming from Japan," Romney said. "I just rejected that argument."

He said he would consider people of any faith, but that they would be selected based on merit.

Romney spokesman Eric Fehrnstrom later pointed out that Ijaz is a Democratic Party fundraiser, and said he carries a partisan political agenda. Ijaz has contributed to Bill Clinton, John Kerry and the Democratic Senatorial Campaign Committee. He also contributed to Hillary Clinton eight years ago.

The conversation recounted in Ijaz's opinion piece, titled "A Muslim belongs in the Cabinet," reportedly took place at a fundraiser in Las Vegas. In the article, Ijaz argued that a high-level Muslim appointee would be effective and sensitive to cultural differences in Islamic societies.

"It is time for (Romney) to reconsider his views on who should help America craft the right policies that attack the scourge on civilization that Islamic extremism has become," he wrote, urging Romney and other candidates to pursue Muslims for cabinet-level posts.

FOX News' Shushannah Walshe contributed to this report.