U.S. President Donald Trump on Wednesday said he placed "no pressure whatsoever" on Ukrainian President Volodymyr Zelensky to investigate Democratic political rival Joe Biden.

Trump commented during a meeting in New York with Zelensky on the sidelines of the annual UN General Assembly as the two were asked about their July 25 telephone call.

A partial transcript of the call, released by the White House on Wednesday, shows Trump repeatedly prodded Zelensky to work with the U.S. attorney general and Trump's personal lawyer to investigate Biden, a former U.S. vice-president and a leading contender for the 2020 federal election.

The call is the subject of a whistleblower complaint made in mid-August against Trump and the basis for Democratic House Speaker Nancy Pelosi's decision on Tuesday to open an impeachment inquiry.

Zelensky said it was a "good phone call" and "normal" and that he and Trump discussed "many things." The Ukrainian leader added, "Nobody pushed me."

U.S. President Donald Trump shakes hands with Ukraine's President Volodymyr Zelensky during a bilateral meeting on the sidelines of the UN General Assembly in New York on Wednesday. (Jonathan Ernst/Reuters)

Trump told the Ukrainian president "If you can look into it ... it sounds horrible to me." Trump was talking about unsubstantiated allegations that Biden sought to interfere with a Ukrainian prosecutor's investigation of his son, Hunter.

"There's a lot of talk about Biden's son, that Biden stopped the prosecution, and a lot of people want to find out about that, so whatever you can do with the attorney general would be great," Trump said in the call, according to the summary.

The call occurred a few days after Trump had ordered the U.S. government to freeze about $391 million in aid to Ukraine, funds that were later released.

Despite the transcript showing Trump's attempts to press Zelensky, the U.S. president reiterated his stance earlier on Wednesday that "there was no pressure whatsoever."

The memo summary also shows that the president referred to the private cybersecurity firm that investigated Russia's hack of the Democratic National Committee servers during the 2016 election. He suggests that Ukraine may be in the possession of the email server, though it's unclear what he's referring to.

Trump also says he'd like to have his attorney general "call you or your people and I would like you to get to the bottom of it."

Pelosi said the notes of the call confirm that Trump engaged in behaviour that undermines the integrity of U.S. elections, the dignity of presidency and American national security.

"The President has tried to make lawlessness a virtue in America and now is exporting it abroad," she said. "It is not part of his job to use taxpayer money to shake down other countries for the benefit of his campaign."

U.S. President Donald Trump, seen here at the UN headquarters in New York City, repeatedly denied having pressured Ukrainian President Volodymyr Zelensky to look into Joe Biden's family. (Carlo Allegri/Reuters)

The comments follow Pelosi's announcement on Tuesday that the Democratic-led House was moving forward with an official impeachment inquiry and directed six committees to proceed with investigations of the president's actions.

"The actions of the Trump presidency revealed a dishonourable fact of the president's betrayal of his oath of office, betrayal of our national security and betrayal of the integrity of our elections," she said on Tuesday.

Trump has withstood repeated scandals since taking office in 2017 and House Democrats had considered, but never moved ahead with, pursuing articles of impeachment over Trump's actions relating to Russian interference in the 2016 U.S. election aimed at boosting his candidacy.

Under the U.S. Constitution, the House has the power to impeach a president for "high crimes and misdemeanours." No president has ever been removed through impeachment. Democrats currently control the House and Trump's fellow Republicans control the Senate.

Biden, who served as U.S. vice-president from 2009 to 2017, is the front-runner for the Democratic presidential nomination. Trump is seeking a second four-year term in the November 2020 election.

The United States has been giving military aid to Ukraine since Russia's annexation of Crimea in 2014. The $391.5 million in aid at issue in the current controversy was approved by the U.S. Congress to help Ukraine deal with an insurgency by Russian-backed separatists in the eastern part of the country.

Joe Biden, Democratic U.S. presidential candidate and former vice-president, says if the reports are true, 'then there is truly no bottom to President Trump's willingness to abuse his power and abase our country.' (Kathryn Gamble/Reuters)

Trump acknowledged Sunday that he discussed Biden and Biden's son, who had worked for a company drilling for gas in Ukraine, with Zelensky​​​​​. On Monday, Trump denied trying to coerce Zelensky in their phone call to launch a corruption investigation into Biden and his son in return for the U.S. military aid.

Trump has offered differing reasons for why he wanted the money for Ukraine frozen, initially saying it was because of corruption in Ukraine and then saying it was because he wanted European countries like France and Germany, not the United States, to take the lead in providing assistance to Kiev.

The current controversy arose after a whistleblower from within the U.S. intelligence community brought a complaint with an internal watchdog relating to Trump's conversation with Zelensky​​. Even though federal law calls for such complaints to be disclosed to Congress, the Trump administration has refused to do so.

Pelosi on Tuesday said Trump's actions had "seriously violated the Constitution," and she accused his administration of violations of federal law.

U.S. intelligence agencies and a special counsel named by the Justice Department previously concluded that Russia boosted Trump's 2016 presidential election bid with a campaign of hacking and propaganda aimed at harming his Democratic opponent Hillary Clinton.

Potential campaign finance violation

The intelligence community's inspector general told the acting director of national intelligence that the call between Trump and Zelensky could have been a federal campaign finance violation.

But the Justice Department determined the president did not commit a crime after prosecutors reviewed the rough transcript of the July 25 call.

A Justice Department official says the inspector general suspected that the call could have broken federal law if the president was soliciting a campaign contribution from a foreign government by asking the Ukraine leader to investigate a political opponent.

The official says that was based on the whistleblower's complaint and the inspector general didn't have access to a rough transcript of the call.

Prosecutors from the Justice Department reviewed a rough transcript of the call and determined the president did not violate campaign finance law.

The official spoke on condition of anonymity in order to discuss internal investigative deliberations.