WASHINGTON — Mick Mulvaney, the acting White House chief of staff, tried again on Sunday to back off assertions he made to reporters last week that the Trump administration had held up an aid package to Ukraine because the president wanted the country to investigate Democrats, acknowledging he did not have a “perfect press conference.”

During an appearance on “Fox News Sunday,” Mr. Mulvaney disagreed with an assertion by the show’s anchor, Chris Wallace, that Mr. Mulvaney’s remarks were proof of a quid pro quo, an exchange the president has publicly denied for weeks. But he struggled to explain how his comments Sunday were not at odds with what he said last week.

“That’s what people are saying that I said, but I didn’t say that,” Mr. Mulvaney said, adding that he had outlined “two reasons” for withholding the aid to Ukraine in a news briefing with reporters on Thursday. In the briefing, however, he outlined three reasons: the corruption in the country, whether other countries were also giving aid to Ukraine and whether Ukrainian officials were cooperating in a Justice Department investigation.

Mr. Wallace played back Mr. Mulvaney’s appearance before reporters in which he said the president’s concern about interference in the 2016 election — and his interest in a widely debunked theory that a Democratic National Committee server is being held in Ukraine — was part of that final reason for withholding aid.