President Trump said Wednesday that the official who blew the whistle on his interactions with Ukraine is politically conflicted and should be “exposed and questioned properly,” taking his three-year fight against the so-called deep state to a new level.

He ratcheted up his calls to unmask the anonymous whistleblower after it was revealed that he had a “professional relationship” with one of Mr. Trump’s potential 2020 Democratic rivals.

“The whistleblower was in cahoots with Schiff,” said Mr. Trump, referring Rep. Adam B. Schiff, California Democrat and chairman of the House Permanent Select Committee on Intelligence. “Then it turns out that whistleblower is a Democrat, a strong Democrat, and is working with one of my opponents, as a Democrat, that I might end up running against. The whole thing is a scam, it’s a fix.”

Mr. Trump also said the whistleblower’s leanings pose a potential conflict of interest. “He or she should be exposed and questioned properly,” he tweeted.

One of the whistleblower’s attorneys, Mark S. Zaid, responded Wednesday evening by saying his client has come into contact with presidential candidates from both parties in their roles as elected officials — not candidates — and “never worked for or advised a political candidate, campaign or party.”

Mr. Trump slammed the unidentified official three days after 90 former national security officials signed an open letter lauding the whistleblower for calling out Mr. Trump’s request for Ukrainian President Volodymyr Zelensky to investigate a Democratic rival, former Vice President Joseph R. Biden, and his son Hunter, who had business ties in Ukraine.

Mr. Biden called Wednesday for the president to be impeached. He said Mr. Trump “is shooting holes in the Constitution, and we cannot let him get away with it.”

The president says he has the right to confront his accuser while insinuating that aides who fed information to the whistleblower are double agents.

“We could have a spy,” Mr. Trump said. “I don’t want to have spies when I’m negotiating with China and Syria and all of the countries.”

Vice President Mike Pence said Mr. Trump’s request for Ukraine to investigate Mr. Biden was in “no way connected” to the president withholding military aid to the country, as far as he knew.

Pressed by reporters in Iowa whether he was “aware” that the military aid was tied to a probe of Mr. Biden, Mr. Pence responded, “That’s your question. Let me be very clear, the issue of aid and our efforts with regard to Ukraine, were from my experience no way connected to the very legitimate concern the American people have about corruption that took place, about things that happened in the 2016 election.”

The episode is shining a bright light on a debate that has raged since Mr. Trump swept into the White House: Are pockets of the nation’s national security and intelligence apparatus intent on undermining an unconventional administration, or is Mr. Trump unfairly discrediting officials who call it like they see it — and are alarmed by what they see?

“Donald Trump has shown himself to be incompetent at times on foreign policy, and the people who see that most clearly work in the foreign policy and intelligence communities. They know it and don’t like it, and when they speak out about it, he calls them the ‘deep state,’” one former high-level intelligence official said. “I don’t think there is any deep state. It’s a convenient way for the president’s supporters to torpedo any legitimate criticism of him.”

Mr. Trump and his allies insist the deep state is real and kicking into overdrive as the Ukraine scandal threatens to envelop the White House.

“This is looking more & more like a deep state scheme,” House Minority Whip Steve Scalise, Louisiana Republican, tweeted this month. He accused Mr. Schiff of plotting with the whistleblower.

Mr. Trump says it’s not just government. He recently suggested Big Pharma might be gunning for him, too.

“We’re lowering the cost of prescription drugs, taking on the pharmaceutical companies. And you think that’s easy? It’s not easy,” Mr. Trump told seniors in The Villages, Florida, last week. “They come at you from all different sides. I wouldn’t be surprised if the hoax didn’t come a little bit from some of the people that we’re taking on.”

Mr. Trump’s suspicions are rooted in questions about his 2016 election victory. Mr. Trump is disgusted by the idea that his upset win was abetted by Russia. He said his unique brand of campaigning and populist message led to one of the most stunning political victories of all time.

“For the last three years, Democrat lawmakers, their deep state cronies, the fake news media, they’ve been colluding in their effort to overturn the presidential election — 63 million people voted — and to nullify the votes of the American people,” Mr. Trump told young black conservatives at the White House this month.

Mr. Trump accused intelligence agencies in January 2017 of adopting tactics from Nazi Germany and, about a week later, boasted about himself in front of a wall honoring fallen Central Intelligence Agency officers at Langley, Virginia.

At a low point during a mid-2018 press conference in Finland, Mr. Trump seemed to accept Russian President Vladimir Putin’s denial about 2016 election meddling over the U.S. intelligence community’s conclusions.

Although those moments are memorable, some say the disconnect between Mr. Trump and the intelligence community is philosophical.

“What they’re disagreeing on is the process,” Republican strategist Ford O’Connell said. “He is changing the way that we look at things, and to them that’s kind of a problem because they like the idea of, ‘We’re going to see this in a certain way.’”

The whistleblower episode illustrates the divide.

The complaint cried foul over entreaties that Mr. Trump’s personal attorney, Rudolph W. Giuliani, made to Ukrainian officials and flagged Mr. Trump’s call with Mr. Zelensky. The document said the president used the phone call to “advance his personal interests” and that White House officials were “deeply disturbed” by what transpired.

Michael Atkinson, the inspector general for the intelligence community, deemed the complaint urgent and credible.

Mr. Trump insists his tactics on the call were “perfect” and that the Ukrainian probe amounts to hoax 2.0 after special counsel Robert Mueller’s investigation found no criminal conspiracy between his campaign and Russia.

Mr. Trump riffed on his victimization repeatedly as he signed an unrelated pair of executive orders Wednesday to alleviate regulatory burdens on small businesses and families.

“No American should ever face such persecution from their own government,” he said at the White House. “Except, perhaps, your president.”

The Justice Department has tasked U.S. Attorney John Durham with exploring the origins of the Russia probe, a mission that White House allies refer to as “investigating the investigators.”

The president’s latest fixation, however, is on Mr. Atkinson and the whistleblower.

“The Whistleblower has ties to one of my DEMOCRAT OPPONENTS. Why does the ICIG allow this scam to continue?” Mr. Trump tweeted.

Sen. Tom Cotton, Arkansas Republican, accused Mr. Atkinson on Wednesday of playing it coy in Sept. 26 testimony to the Senate Select Committee on Intelligence.

“You moralized about how you were duty bound not to share even a hint of this political bias with us,” he said. “But now I see media reports that you revealed to the House intelligence committee not only that the complainant is a registered Democrat, but also that he has a professional relationship with a Democratic presidential campaign.”

Former U.S. national security officials said in their letter Sunday that Mr. Trump and his allies must leave the whistleblower alone.

“While the identity of the whistleblower is not publicly known, we do know that he or she is an employee of the U.S. government,” they wrote. “As such, he or she has by law the right — and indeed the responsibility — to make known, through appropriate channels, indications of serious wrongdoing.”

• Guy Taylor and Dave Boyer contributed to this report.

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