KYIV, Ukraine — President Donald Trump's personal lawyer Rudy Giuliani met Thursday in Ukraine with a key figure working to build a corruption case against Hunter Biden, the Ukraine lawmaker said, after posting Facebook photographs of himself with the former New York mayor.

Andriy Derkach said he pressed Giuliani on the need to set up a joint U.S.-Ukraine investigation into corruption in Ukraine at the meeting in Kyiv. Derkach also vowed to set up an anti-corruption group in the Ukraine parliament.

Giuliani did not make any public comments on the meetings in Ukraine.

But, in tweets hours later, Giuliani drew connections between future U.S. aid and investigations by Ukraine into former vice president Joe Biden — issues that are already at the center of the impeachment inquiry.

Giuliani tweeted that U.S. assistance to Ukraine on anti-corruption reforms could face a "major obstacle" until the "conversation about corruption in Ukraine" is resolved. Giuliani alleged "compelling" evidence of criminal misdeeds by Biden, but he gave no specifics.

His presence in Ukraine also advances the efforts of Trump allies to create an alternative narrative in the rapidly moving impeachment investigation — tapping some of Ukraine's most controversial figures who have spread theories of corruption and impropriety around Joe Biden, his son Hunter Biden and Ukrainian interference in the 2016 election.

The New York Times, which first reported Giuliani's travels, said he had meetings in Budapest and Kyiv this week to meet current and former Ukrainian officials for a documentary.

Derkach noted that their meeting was filmed by "some kind of American television company" but offered no further details.

"Rudolph Giuliani has arrived in Kyiv. We met up immediately to discuss the establishment of the Friends of Ukraine STOP Corruption interparliamentary group," Derkach said in a Facebook post.

Derkach, an independent lawmaker who was formerly a member of a pro-Russian party in parliament, went to the Dzerzhinsky Higher School of the KGB in Moscow. He is the son of a KGB officer who later served as head of Ukrainian intelligence.

Derkach wrote that Giuliani could help bring experts, journalists and analysts to investigate corruption in Ukraine and "benefit strategic relations between Kyiv and the United States."

Derkach said he had sent letters Tuesday to key Republicans including South Carolina Sen. Lindsay Graham, California Rep. Devin Nunes and White House acting chief of staff Mick Mulvaney, seeking their participation.

He said their involvement would help expose the ineffective use of U.S. tax dollars by Ukrainian authorities.

"We sent our proposal. We're waiting for a reaction, an answer. We're waiting to see how much this is something that the congressmen and senators are in need of. If they want to work together, we're ready," Derkach said.

Derkach said he handed Giuliani documents outlining allegations relating to inefficient expenditure of U.S. government money on projects in Ukraine and other matters.

The documents do not specifically mention the Bidens. But Derkach makes reference to the energy company Burisma, which had Hunter Biden as a board member.

Right-wing network One America News announced Tuesday it was conducting a "special investigation" with Giuliani, flying three Ukrainian officials to the United States and "debunking Schiff's impeachment narrative."

Rep. Adam Schiff, D-Calif., chaired the House Intelligence Committee that handed down a report concluding that Trump sought to undermine U.S. democracy and endangered national security.

Derkach did not state whether the TV crew with Giuliani was from One America News.

Derkach and another parliamentary deputy, Oleksandr Dubinsky, called a news conference last month in Kyiv announcing plans to launch an investigative committee of the Ukrainian parliament, claiming corruption by top Ukrainian political figures and Burisma.

The company is at the heart of the impeachment investigation, with allegations Trump withheld military aid to press Ukrainian President Volodymyr Zelensky to open corruption investigations that could have damaged Joe Biden, a potential rival in next year's presidential election.

Analysts have dismissed Derkach as spreading disinformation to support the theory, being promoted by Trump allies, that Biden sought the dismissal of a former Ukraine prosecutor general, Viktor Shokin, because he wanted to protect his son.

Ukraine's prosecutor general, Ruslan Ryaboshapka, said in early October that he would carry out an audit to review the handling of all previous cases involving Burisma.

No evidence of wrongdoing by the Bidens has emerged, and European powers were also seeking Shokin's dismissal, seeing him as corrupt and an obstacle to reform.

Derkach has previously led calls to investigate the Bidens and alleged Ukrainian interference in the 2016 U.S. presidential elections. In 2017, he wrote a letter to the Ukrainian prosecutor general's office, demanding an investigation into alleged interference in the elections by Ukrainian officials to hamper Trump's campaign, claiming this had "seriously damaged Ukraine-American relations."

The July 24, 2017, letter came one day before Trump called on the U.S. attorney general's office in a tweet to investigate "Ukrainian efforts to sabotage the Trump campaign."

Derkach and Dubinsky, however, seem to be experiencing difficulty attracting the support of 150 members of parliament - the number required to form the investigative group.

Derkach and Dubinsky have "zero" chance of forming an investigative committee, said one parliamentarian Thursday, who spoke on the condition of anonymity because of the sensitivity of the issue.

Anders Aslund, a senior fellow at the Atlantic Council and analyst on corruption in Russia and Ukraine, tweeted last month that Derkach and others were spreading "lies" on behalf of Trump and Giuliani.

"Stay away from them! All lies!" he wrote.

He tweeted Wednesday that Giuliani "has chosen Ukrainian interlocutors who are criminals & NEVER say anything true."

On Tuesday, Giuliani met again with another key figure, former Ukrainian prosecutor Yuri Lutsenko, in Budapest, according to the New York Times. Giuliani had met previously with Lutsenko, who also has pushed the theory that Ukraine, not Russia, intervened in 2016 elections.

The New York Times reported Giuliani was seeking other meetings with two former prosecutors, Shokin and Kostiantyn Kulyk.

Ukrainian anti-corruption campaigner Daria Kaleniuk, director of the nonprofit Anti-Corruption Action Center, described Derkach on Twitter as having associations with Ukrainian security services and an allegedly corrupt pharmaceutical firm. She noted that he opposed a system of electronic declaration of parliamentarians' assets in 2015, designed to clean up endemic Ukrainian corruption.

Dixon reported from Moscow. The Washington Post's Colby Itkowitz in Washington contributed to this report.