Mr. Giuliani’s associates, Lev Parnas and Igor Fruman, pitched their new company, and plans for a Poland-to-Ukraine pipeline carrying U.S. natural gas, in meetings with Ukrainian officials and energy executives this year, saying the project had the support of the Trump administration, according to people briefed on the meetings. In many of the same meetings, the two men also pushed for assistance on investigations into Democratic presidential candidate Joe Biden and alleged interference by Ukraine in the 2016 U.S. election, some of the people said.

In conversations that continued into this summer, Messrs. Parnas and Fruman told Ukrainian officials and others that Mr. Giuliani was a partner in the pipeline venture, which was a project of their company, Global Energy Producers, one of the people said. Another person said the men considered Mr. Giuliani a prospective investor in their company more broadly, but said the pitch was unsophisticated and exaggerated.

In an interview Friday, Mr. Giuliani vehemently denied any involvement in the energy company or the pipeline pitch. “I have no personal interest in any business in Ukraine, including that business,” Mr. Giuliani said, adding that he had no indication if prosecutors were looking into the matter. “If they really want to know if I’m a partner, why don’t they ask me?”

The Ukrainians understood the pipeline to be “part of the essential package” Mr. Giuliani and his associates were pushing, often mentioned immediately after the demand for investigations, said Kenneth F. McCallion, a New York lawyer who represents a number of Ukrainian individuals who learned of the pipeline deal, including former Prime Minister Yulia Tymoshenko, who left office in 2010.

The Wall Street Journal has previously reported that prosecutors are scrutinizing Mr. Giuliani’s business dealings in Ukraine, including his finances, meetings and work for a city mayor in Ukraine. The inquiry grew out of a campaign-finance investigation into Messrs. Parnas and Fruman, people familiar with the investigation said. The Soviet-bloc born businessmen, both U.S. citizens based in Florida, were arrested last month on charges that they conspired to funnel foreign money to U.S. politicians and made illegal contributions of their own. They have pleaded not guilty.

Prosecutors are considering whether Mr. Giuliani may have violated lobbying laws in connection with his Ukraine work, people familiar with the investigation said. It couldn’t be determined what criminal charges, if any, prosecutors would weigh in connection with Mr. Giuliani’s alleged interest in Global Energy Producers.

“I don’t know what they said to other people about me,” Mr. Giuliani said Friday, referring to Messrs. Parnas and Fruman. “I do know the following: I am not a part of the ownership, or any other involvement with GEP. I never agreed to be part of it. I’m not even sure I was ever asked to be part of it.” He said that if Messrs. Parnas and Fruman had asked for his legal opinion, he would have told them to avoid involvement in any “ownership situation” in Ukraine while working alongside him there, because it would look “stupid.”

Mr. Giuliani, the president’s lawyer, previously has denied wrongdoing and said he was acting in Ukraine on behalf of Mr. Trump. Mr. Giuliani has also said he provided Messrs. Parnas and Fruman “civil advice on business.” Friday he said he had also referred Global Energy Producers to another lawyer in connection with campaign-finance issues.

Mr. Giuliani has said his efforts in Ukraine were coordinated with the State Department.

Mr. Giuliani’s work for Mr. Trump and the pressure campaign in Ukraine are central to an impeachment inquiry that began its public phase on Wednesday in the House of Representatives.

In the first public testimony in the impeachment proceedings this week, U.S. officials said Mr. Giuliani opened an irregular channel of diplomacy in Ukraine, pressing for investigations that could help Mr. Trump politically. At the same time, the Trump administration withheld military aid to Ukraine temporarily, in what Democrats say was an inappropriate quid pro quo.

Mr. Trump has called the impeachment inquiry a hoax and said his dealings with the Ukrainian government were proper.

Messrs. Fruman and Parnas have been closely involved with Mr. Giuliani’s Ukraine-related work in the past year, including introducing Mr. Giuliani to Ukrainians and lobbying former Ukrainian President Petro Poroshenko to open investigations that Democrats say would benefit President Trump.

In meetings with officials and businessmen in Ukraine, Messrs. Parnas and Fruman typically presented a number of interconnected demands, according to people familiar with the conversations. They pressed for Ukraine’s leaders to announce investigations into Mr. Biden and into unfounded theories that Ukraine had played a role in interfering in the 2016 elections.

Mr. Giuliani and others close to Mr. Trump have called for investigations into Mr. Biden and his son, Hunter Biden, related to the younger Biden’s time on the board of Burisma Group, a Ukrainian gas company. Mr. Biden has denied wrongdoing, and Ukraine’s former top prosecutor has said there was no evidence of a crime.

They also talked up their company, Global Energy Producers, and a plan to ship U.S. natural gas to Ukraine. The project had many practical impediments—including geography and cost—but had the potential to be extremely lucrative, people familiar with the pitch said. It would need the support of Ukrainian officials and a partnership with Naftogaz, the state-owned energy company.

Messrs. Parnas and Fruman presented themselves, and the pipeline deal, as having the backing of Mr. Giuliani and the Trump administration, according to people familiar with the conversations. They also told Ukrainian officials and others that the project had the backing of Dmytro Firtash, a Ukrainian tycoon who made his fortune brokering natural-gas sales from Russia and Central Asia to Ukraine.

The Trump administration has long promoted U.S. liquefied natural gas, dubbed “freedom gas,” as a way for Europe to reduce its reliance on Russia for energy.

Mr. Firtash, who is in Vienna fighting extradition to the U.S. to face bribery and related charges, has aligned himself in recent years with people close to Mr. Trump and Mr. Giuliani. Mr. Firtash has denied the allegations.

A spokesman for Mr. Firtash’s legal team said in a statement: “Mr. Firtash met Mr. Parnas for the first time in June 2019. Mr. Firtash had no business relationship with Mr. Parnas or Mr. Fruman.” The law firm representing Mr. Firtash, diGenova & Toensing, hired Mr. Parnas this summer to serve as an interpreter, the firm has said.

One potential snag for the proposed pipeline was Naftogaz, the dominant player in Ukrainian energy and a focal point of U.S. foreign policy in the region. One person familiar with the Naftogaz board said the company dismissed Global Energy Producers’ proposed pipeline as impractical.

Messrs. Fruman and Parnas devised a plan to facilitate the pipeline plan by replacing Naftogaz’s chief executive, the Journal and others have previously reported. As part of that plan, in March, they approached a senior Naftogaz executive with a proposal to install him as the head of the company, a former business partner of the executive told the Journal.

Efforts by Trump administration officials and associates to install new management at Naftogaz, in hopes of steering contracts to companies controlled by Trump allies, have also been described by the Associated Press.

—Rebecca Ballhaus, Christopher M. Matthews and Georgi Kantchev contributed to this article.

Write to Rebecca Davis O’Brien at Rebecca.OBrien@wsj.com