Mounting evidence released amid the ongoing presidential impeachment hearings indicates that the pressure President Trump and his aides put on Ukraine was driven by a focus on his political rivals, even as Trump’s defenders say the president was acting out of general concern about corruption in that country.

The White House is emphasizing that argument anew as the defense makes its case in the Senate trial.

“Asking a foreign leader to get to the bottom of issues of corruption is not a violation of an oath,” Jay Sekulow, an attorney for Trump, told the senators Monday.

But that assertion was dramatically undercut by reports Sunday about a draft book manuscript by former national security adviser John Bolton. In it, he recounts that Trump told him he was holding up military aid to Ukraine until the country’s leaders agreed to open investigations into Democrats, including former vice president Joe Biden, according to people familiar with the book.

Trump has denied that account, which was first reported by the New York Times, tweeting Monday, “I NEVER told John Bolton that the aid to Ukraine was tied to investigations into Democrats, including the Bidens.”

“The transcripts of my calls with President Zelensky are all the proof that is needed,” he added.

But a rough transcript of the July call released by the White House shows that Trump specifically urged the Ukrainian president to pursue two investigations: one into the Bidens and the other into a discredited theory involving an Internet security company that probed the Democratic National Committee hack in 2016.

He never mentions the word “corruption,” the transcript shows.

Text messages and congressional testimony also show that, behind the scenes, the president’s envoys repeatedly rejected efforts by Ukrainian officials to commit to broadly cracking down on corruption — insisting instead that their public statements mention the Ukrainian gas company where Biden’s son was on the board and allegations about Ukrainian interference in the 2016 U.S. presidential election.

In exchange, the Ukrainians were hoping to secure a coveted meeting at the White House for President Volodymyr Zelensky, which has still not occurred.

Trump’s allies have suggested that a president concerned about corruption would be irresponsible to ignore the allegations of wrongdoing about Biden. However, the president only began speaking out about the role of Biden’s son on the board of a Ukrainian gas company after the former vice president emerged as a potential 2020 rival.

While Trump has fixated on Biden, he has expressed sympathy for his former campaign chairman, Paul Manafort, who pleaded guilty to failing to pay taxes on $30 million he earned in political consulting fees in Ukraine, where he worked with an array of officials around former Ukrainian President Viktor Yanukovych who fled the country amid corruption accusations.

Trump has repeatedly said in recent months that he was urging Ukraine to look at corruption broadly.

“I don’t care about Biden’s campaign, but I do care about corruption,” he told reporters outside the White House in October.

The president reiterated that in recent weeks, telling reporters at his Florida resort on Jan. 1, “We did nothing wrong,” adding: “We have to check corruption.”

His Republican allies have echoed that argument.

“A president always has the constitutional authority and in fact, the responsibility to investigate serious evidence of corruption,” Sen. Ted Cruz (Tex.) said Monday.

However, the political aim of the Ukraine pressure campaign is underlined in the newest batch of text messages released by the House from Lev Parnas, a onetime associate of Trump’s personal attorney, Rudolph W. Giuliani.

The messages show a concerted effort to secure statements regarding Biden from then-Ukrainian President Petro Poroshenko and then-Ukrainian Prosecutor General Yuri Lutsenko for U.S. news outlets, just as special counsel Robert S. Mueller III geared up to release his report about Russian interference and Biden prepared to announce his presidential run.

At one point, Lutsenko wrote to Parnas that he was prepared to “screw over your opponent,” in an apparent reference to Biden.

Texts between the two men also show they discussed a clear deal: In exchange for making the damaging statements about Biden, Lutsenko was seeking the ouster of the then-U.S. Ambassador to Ukraine Marie Yovanovitch, as well as a visit to the United States to meet Attorney General William P. Barr and other unspecified help for his boss, Poroshenko, who was fighting for his political life in a presidential election he would ultimately lose.

The messages show that Giuliani became angry when Lutsenko reversed his previous public suggestions of wrongdoing by Biden.

None of the exchanges between the men make mention of U.S. aims to end corruption in Ukraine.

In an interview with The Washington Post, Parnas said that Giuliani emphasized the importance of the Ukrainians singling out Biden in a face-to-face meeting with Zelensky adviser Andriy Yermak in the lobby of a five-star luxury hotel in Madrid in early August.

“They had to include a statement about Burisma and Biden,” said Parnas, who was at the meeting.

Burisma is a gas company owned by a former Ukrainian government minister accused by authorities and anti-corruption activists there of abusing his office to build his energy fortune. ​Hunter Biden served on the firm’s board from 2014 to 2019.

Parnas’s account matches what Giuliani told The Post in September, when he said that he urged Yermak to pursue investigations into Burisma and alleged coordination between Democrats and Ukrainians in 2016.

“Your country owes it to us and to your country to find out what really happened,” Giuliani said he told Yermak during the Madrid meeting.

Yermak, according to Giuliani, indicated that the Ukrainians were open to pursuing the investigations. The aide reiterated the Ukrainians’ plea for a meeting with Trump, a summit that would be an important signal to Russia of Washington’s support for Ukraine.

Parnas said Giuliani told Yermak that he planned to follow up with two U.S. diplomats, Kurt Volker and Gordon Sondland, and that the three Americans would discuss the precise wording of Zelensky’s statement.

“They were supposed to work it out,” Parnas said.

After the Madrid meeting, Yermak texted Volker that the Ukrainians would announce probes into Burisma, as well as the 2016 election, according to messages released by House investigators.

“Once we have a date, will call for a press briefing, announcing upcoming visit and outlining vision for the reboot of US-UKRAINE relationship, including among other things Burisma and election meddling in investigations,” he wrote.

“Sounds great!” Volker responded.

But two days later, Yermak sent Volker a draft statement that referred only generally to “the problem of interference in the political processes of the United States,” text messages show.

Volker and Sondland consulted with Giuliani on the statement. The president’s lawyer did not find it “convincing,” Volker recalled in his testimony.

“Mr. Giuliani was the one giving the input as to what the president wanted in the statement. He wanted Burisma and 2016 election mentioned in the statement. And I don’t believe the Ukrainians were prepared to do that,” Sondland told House investigators.

In a group text with Sondland, Volker sent new language to Yermak that included an “insert at the end for the 2 key items” — specific references to Burisma and the 2016 election.

But privately, Volker said, he warned Yermak that releasing the statement “was not a good idea” and could entangle the Ukrainians in U.S. domestic politics.

“Because of conversations with Giuliani, I wanted to make sure that I was cautioning the Ukrainians, ‘Don’t get sucked in,’ ” Volker recounted.

​The Ukrainians ultimately did not release the statement — and Zelensky has still not received an official White House meeting.

Meanwhile, U.S. officials grew increasingly concerned that Trump was holding back more than $300 million in military assistance to Ukraine until Zelensky agreed to open the Biden investigation.

Trump has denied linking the two issues. But people familiar with Bolton’s new book say that the former adviser says he was told by the president in August that Ukraine would not get the aid without complying.

Text messages released by the House show that the pressure on Ukrainian officials to make a statement about Trump’s Democratic opponents began in early 2019, before Zelensky’s election.

Texts written in Russian show Lutsenko urging Parnas early last year to force out Yovanovitch in exchange for cooperation regarding Biden. At one point, Lutsenko suggested he wouldn’t make any helpful public statements unless “madam” is removed.

“It’s just that if you don’t make a decision about Madam — you are calling into question all my declarations. Including about B,” Lutsenko wrote to Parnas in a March 22 message on WhatsApp.

It’s unclear if “B” is a reference to Biden or Burisma.

Four days later, Lutsenko told Parnas that work on the case against the owner of the gas company was proceeding successfully and evidence of the money transfers of “B” had been obtained.

“And here you can’t even remove one fool,” Lutsenko laments, using a sad-face emoticon as he again appeared to push for Yovanovitch’s ouster.

“She’s not a simple fool[,] trust me,” Parnas responded. “But she’s not getting away.”

Yovanovitch was called back to Washington in late April and removed from her post about a month later.

The messages show that Lutsenko became frustrated as the ambassador remained in her post for months, and Parnas failed to get him a meeting with Barr and help Poroshenko.

Lutsenko wrote on March 13 that he was “sick of this,” using an expletive. “I haven’t received a visit,” he added. “My boss hasn’t received jack. I’m prepared to screw over your opponent. But you just want more and more. We’re over. I’ll deal with you later. This isn’t honest.”

After Poroshenko lost, putting Lutsenko’s political future in doubt, he gave an interview to Bloomberg News saying there was no evidence of wrongdoing by the Bidens in Ukraine.

Giuliani became incensed, the text messages show. Parnas immediately texted Lutsenko: “911 911 call me.” He demanded to see Lutsenko in person in the middle of the night.

“Yura tell me where I should come I have to see you urgently,” Parnas wrote in a frenzy, using a nickname for Yuri. “Yura it is very very very important.”

When Lutsenko said he was 30 kilometers outside Kyiv and asked to talk by phone, Parnas replied: “I have no choice i really need very important to speak with you very important and Because Rudy really wants to speak with you today with me it’s really important. Trust me I don’t want to go 30 km right now.”

They discussed where to meet before Lutsenko reluctantly agreed to come to Parnas.

Toluse Olorunnipa, Seung Min Kim and Erica Werner contributed to this report.