WASHINGTON — President Trump on Saturday dismissed news reports that he urged the Ukrainian president to investigate former Vice President Joseph R. Biden Jr.’s son as little more than a “witch hunt” and said his dealings were “perfectly fine” and routine.

“Now that the Democrats and the Fake News Media have gone ‘bust’ on every other of their Witch Hunt schemes, they are trying to start one just as ridiculous as the others, call it the Ukraine Witch Hunt,” Mr. Trump wrote on Twitter. He said that any effort to investigate him would fail, comparing it to the investigation by Robert S. Mueller III, the special counsel, into his ties to Russia during the 2016 campaign.

The news reports he was referring to have revealed the existence of a secret whistle-blower complaint that is believed to have been filed, at least partly, in response to Mr. Trump’s dealings with Ukraine’s new president, Volodymyr Zelensky. The New York Times reported Friday that Mr. Trump, in a July call, pressed the Ukrainian president to investigate Mr. Biden’s son, according to a person familiar with the conversation.

Mr. Trump, intensifying a line of attack he and his allies have stoked for months, said the real problem was Mr. Biden, who according to most polls is the leading candidate in a crowded Democratic field and has framed himself as the most likely to defeat Mr. Trump in the general election.