A private lawyer for US President Donald Trump has denied damning allegations made by his ex-FBI director James Comey under oath, and suggested the ousted lawman should be prosecuted for leaking "privileged information."

The president, said Marc Kasowitz, "never told Mr Comey 'I need loyalty, I expect loyalty' in form or substance," rejecting a key allegation made by the sacked FBI director before a Senate panel today.

Rejecting key parts of Mr Comey's testimony while claiming others as a win for the president, Mr Kasowitz also suggested Mr Comey may face prosecution.

"Today, Mr Comey admitted that he leaked to friends his purported memos of these privileged conversations, one of which he testified was classified."

"We will leave it the appropriate authorities to determine whether this leaks should be investigated along with all those others being investigated."

Earlier, Mr Trump rallied die-hard supporters behind a message of defiance.

Without referring to Mr Comey's sworn Senate testimony directly, Mr Trump vowed to fight his enemies and knock back attempts to derail his presidency.

They will "not divert us from this righteous cause, to try and stop all of you," Mr Trump told a Faith and Freedom Coalition event in the US capital Washington DC.

"We know how to fight better than anybody, and we never, ever will give up. We don't give up and we are winners and we are going to fight and win and we will have an unbelievable future."

Mr Comey told a Senate panel that Mr Trump asked him for "loyalty" and asked him to shelve an investigation into aide Mike Flynn.

Mr Comey also accused the Trump administration of lying and defaming him and the FBI in a bid to justify the president's actions.

The White House angrily denounced that charge.

"I can definitely say the president is not a liar and frankly am insulted by that question," White House spokeswoman Sarah Huckabee Sanders said during a briefing at the White House.

Mr Trump was equally combative.

"They will lie, they will obstruct, they will spread their hatred and their prejudice, we will not back down from doing what is right."

People "will get the change they voted for and which they so richly deserve."

"We are going to fight and win" Trump said, addressing supporters at a Faith and Freedom Coalition event in the capital.