The president and his close allies also escalated their attacks on Biden on Sunday, demanding probes into the former vice president and his son’s work in Ukraine, though no evidence has surfaced that Biden acted inappropriately and Trump’s allies did not provide any.

Across several networks Sunday, top administration officials, outside advisers and lawmakers close to Trump repeatedly raised the specter of impropriety on the part of Biden, whose younger son, Hunter, was on the board of a Ukrainian gas company that Trump pushed Ukrainian President Volodymyr Zelensky to investigate, according to people familiar with the matter.

The issue has surfaced because of an extraordinary whistleblower complaint, first reported by The Washington Post. According to people familiar with the matter, Trump pressed Zelensky to dig up potentially damaging information against Biden during a July 25 phone call.

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In an exchange with reporters outside the White House before departing for events in Texas and Ohio on Sunday, Trump appeared to suggest he did speak about Biden with Zelensky.

“The conversation I had was largely congratulatory, was largely corruption, all of the corruption taking place, was largely the fact that we don’t want our people, like Vice President Biden and his son, creating to the corruption already in the Ukraine,” Trump told reporters Sunday morning. “And Ukraine, Ukraine’s got a lot of problems.”

Later in Houston, Trump appeared to backtrack, saying, “I don’t even want to mention it, but certainly I’d have the right to” raise Biden’s name with Zelensky. He also said he would “love” to release a transcript, though he added he would have to make a determination about how to do so.

In his comments, Trump also continued to suggest, with no evidence, that Biden had acted inappropriately.

“I’m not looking to hurt him with respect to his son,” Trump said after landing in Houston on Sunday. But he continued, “Joe’s got a lot of problems. Joe’s got enough problems. But what he said was a terrible thing,” suggesting Biden had lied about communications with his son about Ukraine.

The sentiment was echoed by his senior advisers, who repeatedly suggested, without evidence, wrongdoing on Biden’s part and pushed for the highest levels of the federal government to probe the connections between the former vice president and Ukraine.

Secretary of State Mike Pompeo, speaking on multiple Sunday shows, said he hasn’t seen the whistleblower complaint or news reports about it but raised questions about whether the former vice president acted properly.

“I do hope that if Vice President Biden engaged in behavior that was inappropriate, if he had a conflict of interest or allowed something to take place in Ukraine, which may have interfered in our elections in 2016, I do hope that we get to the bottom of that,” Pompeo said on “Fox News Sunday.”

There is no evidence that Biden played any role in election interference efforts by foreign governments in 2016. Intelligence agencies have concluded that Russia did interfere on behalf of Trump, a fact the president continues to deny.

Since the spring, Rudolph W. Giuliani, the president’s personal attorney, has pushed the Ukrainians to pursue two investigations: one into a gas tycoon who had Hunter Biden on his board and another into his allegations that Democrats colluded with Ukraine to release information on former Trump campaign chairman Paul Manafort during the 2016 election.

On Sunday, Giuliani attacked Joe Biden in deeply personal terms by referencing Hunter Biden’s struggles with addiction.

“The kid, unfortunately, is a drug addict,” Giuliani said on “Fox News Sunday.”

The episode — which broke open Wednesday when The Post reported that a showdown between the intelligence community and Capitol Hill involved Trump’s communications with a foreign leader — has raised questions about the president’s alleged willingness to cooperate with another country for his political gain just months after the official conclusion of former special counsel Robert S. Mueller III’s investigation into potential conspiracy between Trump associates and Russia.

The continued revelations also have given more ammunition to congressional Democrats itching to pursue impeachment proceedings against Trump, demanding that lawmakers hold the president accountable for his behavior even as their own leadership has remained reluctant.

The episode threatens to overshadow much of Trump’s agenda at the United Nations General Assembly in New York, where he arrived Sunday after events in Texas and Ohio. Trump and Zelensky will meet Wednesday, the final day of the president’s activities at the United Nations, in a summit that a senior administration official has said will focus on Zelensky’s anti-corruption efforts there.

Giuliani told The Post on Sunday morning that he has been “working for months for this moment” and this week will “keep pushing and pushing” to highlight the Biden family’s finances.

When asked whether Trump has given Giuliani’s efforts his blessing, Giuliani said, “I don’t do anything that involves my client without speaking with my client.”

Trump also on Sunday took aim at Biden for saying that he never spoke with his son about his overseas business dealings. “He said he never spoke to his son,” Trump said. “Does anybody believe that one?”

Trump has repeatedly insisted that he did not speak to his son Donald Trump Jr. in advance of a June 2016 Trump Tower meeting at which Russians offered to provide Trump’s son with dirt on Democratic nominee Hillary Clinton.

While campaigning Sunday in Kansas City, Biden deflected questions about whether he had spoken to his son about his business dealings in Ukraine, telling reporters: “Focus on the violation of the Constitution this president is engaged in.”

Earlier in the weekend, Biden decried Trump’s efforts as an “abuse of power” and said the president was doing so because “he knows I will beat him like a drum.”

News of Trump’s call with Zelensky came to light after an intelligence official shared with the intelligence community’s inspector general that the official had heard Trump make a promise to a foreign leader that wasn’t appropriate.

Subsequent reporting has found that the call was with Ukraine and related to Trump’s desire to get dirt on his possible political opponent. Congress has not been provided a copy of the actual complaint filed by the whistleblower.

Though most Republicans have tried to sidestep the growing controversy, Sen. Mitt Romney (R-Utah) urged that more details of the Trump-Zelensky call be made public.

“If the President asked or pressured Ukraine’s president to investigate his political rival, either directly or through his personal attorney, it would be troubling in the extreme,” Romney, the party’s presidential nominee in 2012, tweeted Sunday. “Critical for the facts to come out.”

Other senior Republicans played down questions surrounding Trump’s behavior.

Sen. John Cornyn (R-Tex.) said there is “no direct evidence” that Trump asked Zelensky to investigate Biden or his family, saying the allegation is “based on hearsay reports.”

“I just frankly can’t imagine why people have lost their minds so much over these daily reports of one thing or another that seem to consume everybody’s attention in the news coverage,” Cornyn told reporters ahead of the “Howdy, Modi!” forum in Houston, in which Trump appeared with Indian Prime Minister Narendra Modi.

On NBC News’s “Meet the Press,” Treasury Secretary Steven Mnuchin repeatedly declined to say whether it was appropriate for the president to ask a foreign leader to investigate a political rival and suggested that Trump did not pressure Zelensky.

“You’re speculating that the president pressured. I don’t have any reason to believe that the president pressured . . . in any way,” Mnuchin said.

In his “Meet the Press” interview, Mnuchin argued that rather than focusing on “confidential discussions” between two world leaders, “I really think that the real issue here is not what the president said but what indeed did Biden’s son do.”

In meetings overseas with Ukrainian officials, Giuliani has pushed for reopening an investigation of Burisma Holdings, the gas company that hired Hunter Biden in 2014 to serve as a board member and adviser while his father was U.S. vice president.

According to the New York Times, he was paid as much as $50,000 some months for his work.

In 2016, then-Vice President Biden traveled to Ukraine to push for the country to sack its top prosecutor, Viktor Shokin. On that trip, Biden said the United States would withhold $1 billion in loan guarantees unless Shokin was removed. Biden’s push was part of a broader international effort to fight corruption in Ukraine, and Shokin had been accused of ignoring major corruption. Shokin, at one point, led an investigation into Burisma Holdings. However, the case had been dormant before the prosecutor’s firing, according to former Ukrainian and U.S. officials, and the U.S. ambassador at the time publicly called for the investigation in Burisma to proceed.

Sen. Lindsey O. Graham (R-S.C.) called for the Justice Department to play a role in the matter, arguing that it should “look at the Biden-Ukraine connection, like we looked at the Trump-Russia connection,” in a reference to Mueller’s Russia probe.

“What relationships, if any, did the Biden world have to the Ukraine? . . . There’s enough smoke here,” Graham said on Fox News Channel’s “Sunday Morning Futures.”