President Donald Trump's son has released an email chain that shows him discussing plans to hear damaging information on Hillary Clinton, which was described as part of a Russian government effort to help Trump in the 2016 election.

In a statement on Tuesday, Donald Trump Jr said he was posting the emails "in order to be totally transparent".

The emails with music publicist Rob Goldstone show that Trump Jr was told that the Russian government had information that could "incriminate" Clinton, Trump's Democratic rival, and her dealings with Russia.

The information, Goldstone wrote, "would be very useful to your father".

"This is obviously very high level and sensitive information but is part of Russia and its government's support for Mr Trump," he added.

"If it's what you say I love it," replied Trump Jr.

Goldstone was seeking to set up a meeting between Trump Jr and a Russian lawyer that later took place at Trump Tower.

The emails posted on Twitter were dated early June.

Their release follows days of evolving accounts from Trump Jr. about the nature of the meeting and its purpose. He posted the emails only after they were obtained by The New York Times.

Allegations of the Trump campaign's ties to Russia have cast a shadow over the president's first five months in office.

'Big deal'

On Monday, the New York Times reported that Trump Jr was offered "compromising" information as part of a "Russian government effort" to help the Trump election campaign.

Trump Jr's New York-based lawyer Alan Futerfas called the Times report "much ado about nothing" in a statement.

Trump Jr met a Russian lawyer, Natalia Veselnitskaya, with the understanding that she would provide damaging information on Clinton, the statement said.

However, the lawyer did not have any meaningful information to offer, the statement said, adding that her comments were "vague, ambiguous and made no sense".

READ MORE: US Senate begins hearing on Russia involvement in US elections

Earlier on Tuesday, Veselnitskaya told NBC's "Today" show that she met with the Trump campaign after she received a phone call from a man she did not know telling her to meet them.

However, she said she did not have information on the Clinton campaign and has never worked for the Russian government.

The top Democrat on the House Intelligence committee has called reports of the meeting "a very big deal".

Representative Adam Schiff told CNN on Tuesday that his committee, which is investigating possible collusion between the Trump presidential campaign and Russia, would summon the participants of the meeting "to get to the bottom of it".

Both Trump's office and the Kremlin said they were unaware that the meeting took place.

This week's revelations come after President Trump and Russian President Vladimir Putin discussed the allegations of election meddling during the summit of leaders from the Group of 20 major economies in Hamburg, Germany.

The Kremlin has denied US intelligence agencies' conclusion that Moscow tried to tilt the election in Trump's favour, using such means as hacking into the emails of senior Democrats.