Ukraine's president Volodymyr Zelensky has rejected accusations he was put under pressure by his US counterpart Donald Trump during a phone call in July, stating the only person in the world who can put pressure on him is his six-year-old son.

"Nobody can put pressure on me because I am the president of an independent state," Zelensky, a former comedian, told reporters in New York, in comments broadcast by Russia 24. "The only one person, by the way, who can put pressure on me ... is my son, who is six years old."

Zelensky's comments came shortly before the transcript of the conversation between the two presidents was released by the White House.

The phone call between the world leaders forms the basis of impeachment proceedings announced by US house speaker Nancy Pelosi, on September 25. "The president has admitted to asking the president of Ukraine to take actions which would benefit him politically," Pelosi stated. 

Democrats are accusing Trump of pressuring Zelensky to investigate the son of Democractic presidential hopeful Joe Biden. In 2014, Hunter Biden was appointed to the board of major Ukrainian gas producer Burisma Holdings, which had been under investigation by Ukraine's prosecutor general. In 2016, then US vice president Joe Biden encouraged the Ukrainian government to fire the prosecutor general who had inherited the investigation, Viktor Shokin, amid corruption allegations. 

Shokin was dismissed later that year. 

In the phone conversation's transcripts,  released by the White House on Wednesday, Trump says: "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. 

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

Zelensky agreed to the request.

Later on Wednesday, Zelensky and Trump were due to meet on the sidelines of the United Nations General Assembly, in New York City, US. The leaders were then due to face reporters' questions on the phone call and the subsequent impeachment proceedings. 

Trump, who has denied he has done anything improper, tweeted he has "authorized the release tomorrow of the complete, fully declassified and unredacted transcript of my phone conversation with President Zelensky of Ukraine."

The Trump phone call has thrust Zelensky into the spotlight. The former comic actor won Ukraine's May 2019 election, partly campaigning on an anti-corruption message. 

Since assuming office, Zelensky has acted on his promises. On Monday, he signed a bill creating a procedure to impeach a sitting Ukrainian president. A key manifesto pledge, the new law states the country's president can be dismissed through impeachment proceedings should they commit "high treason or other felonies."

In an Instagram post released after the bill was signed, Zelensky urged his fellow Ukrainians to "live in accordance with the law." 

"I am starting with myself and signing the law on presidential impeachment that was adopted by the parliament," Zelensky added.