A transcript of a controversial July 25 phone call released by the White House shows that President Donald Trump, who now faces a formal impeachment inquiry, asked Ukrainian President Volodymyr Zelensky to "do us a favour" and said his lawyer and US Attorney-General William Barr would be in touch with Ukraine to unearth information about former US vice-president Joe Biden.

"There's a lot of talk about Biden's son... and a lot of people want to find out about that so whatever you can do with the Attorney-General would be great," Mr Trump said in the unredacted but non-verbatim transcript.

"Biden went around bragging that he stopped the prosecution so if you can look into it... It sounds horrible to me."

Concerns arose following a whistle-blower's complaint that Mr Trump might have pressured the Ukrainian government into investigating Mr Biden's son, Hunter, in return for aid.

The release of the transcript came a day after the opposition Democratic Party announced a formal impeachment inquiry, triggered by the unnamed whistle-blower who had reported the conversation, signalling a long and bruising gloves-off battle going into the 2020 election season.

The President has maintained that there was nothing inappropriate about the call, saying he had stalled almost US$400 million (S$551 million) in aid to Ukraine because he wanted Europe to do more for Ukraine first. "Why is it always the United States that pays?" he told reporters in New York.

The transcript does show Mr Trump criticised Germany for not doing enough for Ukraine. And there is no mention of the American aid.

Mr Trump told reporters in New York that the transcript was a bust, and that it had been built up as the "call from hell" but "it turned out to be a nothing call".

Earlier, he lashed out on Twitter, saying: "The Democrats are frozen with hatred and fear. They get nothing done. This should never be allowed to happen to another President. Witch Hunt!"

On Tuesday, Speaker of the House Nancy Pelosi said Mr Trump's conduct had violated his oath of office and duty under the Constitution.

"The House of Representatives is moving forward with an official impeachment inquiry," she told a press conference. "I'm directing our six committees to proceed with their investigations under that umbrella... The President must be held accountable."

Until then, many Democrats had been reluctant to launch impeachment proceedings, worried that the political backlash would further solidify and inflame Mr Trump's base. But the mood turned as the President appeared to admit that Mr Biden's name had figured in the phone call, even as he denied any quid pro quo offer.

The case he wanted Ukraine to investigate concerned old allegations that Mr Biden had used the influence of his office in 2016 to persuade Ukraine to fire the prosecutor investigating the company, Burisma Holdings, in which his son was involved.

The prosecutor was fired, but the allegations against Mr Biden came to nothing.

If the impeachment inquiry does produce a motion to impeach, the House would need a simple majority to send it to the Senate. But impeachment would require a two-thirds majority in the Senate, which is controlled by the Republican Party. It would need significant desertions by Republicans - currently a highly unlikely scenario - to finally impeach Mr Trump.

Yet, while impeachment is likely to fail ultimately, the process of the inquiry itself gives Congress wide powers.

"This will make it much more difficult for the Trump administration to refuse to hand over documents or refuse to allow people to testify," Dr Glenn Altschuler, professor of American Studies at Cornell University, told The Straits Times.

One of the key reasons why Democrats decided to launch a formal inquiry was frustration with the stonewalling tactics of the White House, he said. Now if the administration goes to the courts, the courts would in all likelihood side with Congress.

Mr Brad Parscale, the Trump 2020 campaign manager, said in an e-mail: "The facts prove the President did nothing wrong. This is just another hoax from Democrats and the media, contributing to the landslide re-election of President Trump in 2020."

Dr Altschuler said it is certainly a high-risk strategy for the Democratic Party. "But what is important is that this gives the Democrats an issue that looks ahead to 2020 and interference in the election, and that will resonate with voters."

Snippets from Trump's conversation with Ukrainian President

Here are excerpts from the transcript of a July 25 phone call between US President Donald Trump and his Ukrainian counterpart Volodymyr Zelensky.

Trump: I would like you to do us a favour though because our country has been through a lot and Ukraine knows a lot about it. I would like you to find out what happened with this whole situation with Ukraine, they saw Crowdstrike... I guess you have one of your wealthy people... The server, they say Ukraine has it. There are a lot of things that went on, the whole situation. I think you are surrounding yourself with some of the same people.

I would like to have the Attorney-General call you or your people, and I would like to get to the bottom of it.

As you saw yesterday, that whole nonsense ended with a very poor performance by a man named Robert Mueller, an incompetent performance, but they say a lot of it started with Ukraine. Whatever you can do, it is very important that you do it if that is possible.

Zelensky: Yes, it is very important to me and everything that you just mentioned. For me as a president, it is very important, and we are open for any future cooperation. We are ready to open a new page on cooperation in relations between the United States and Ukraine...

I also plan to surround myself with great people and in addition to that investigation, I guarantee as the President of Ukraine that all the investigations will be done openly and candidly. That I can assure you.

Trump: Good, because I heard you had a prosecutor who was very good and he was shut down and that is really unfair. A lot of people are talking about that, the way they shut your very good prosecutor down and you had some very bad people involved.

Mr (Rudy) Giuliani is a highly respected man. He was the mayor of New York City, a great mayor, and I would like him to call you. I will ask him to call you along with the Attorney-General. Rudy very much knows what is happening and he is a very capable guy. If you could speak to him, that would be great...

The other thing, there is a lot of talk about (former vice-president Joe) 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. Biden went around bragging that he stopped the prosecution, so if you can look into it... It sounds horrible to me.

Zelensky: I wanted to tell you about the prosecutor. First of all, I understand and I am knowledgeable about the situation. Since we have won the absolute majority in our Parliament, the next prosecutor-general will be 100 per cent my person, my candidate, who will be approved by the Parliament and will start as a new prosecutor in September. He or she will look into the situation, specifically to the company that you mentioned in this issue. The issue of the investigation of the case is actually the issue of making sure to restore the honesty, so we will take care of that and will work on the investigation of the case. On top of that, I would kindly ask you if you have any additional information that you can provide to us, it would be very helpful for the investigation to make sure that we administer justice in our country...