Republican presidential nominee Donald Trump has responded to the women who accused him of groping them by saying their claims are "preposterous".

Following a difficult week for Trump after footage emerged of him making lewd comments about groping women, several women have alleged the GOP nominee touched them inappropriately in reports run by The New York Times (NYT).

"You take a look at these people ... their claims are preposterous, ludicrous and defy logic," Trump told a rally in Florida, reported The Hill.

"These lies come from outlets whose past stories and claims have already been discredited," he added. "The media outlets did not attempt to confirm the most basic facts because even a simple investigation would have shown these were nothing more than false smears."

Since the initial two women spoke with NYT, several other news outlets — including the Palm Beach Post and People magazine — have spoken with a total of four other women, all of whom allege that Trump made unwanted advances and forcibly kissed or touched them.

The billionaire also suggested he would be suing NYT for defamation, demanded they retracted the accusations, and has lawyers currently looking at the case.

However, The New York Times has issued a response to Trump's demand for a retraction and threats of a defamation case in a letter to his lawyer.

The letter, made available by The New York Times, states: "The essence of a libel claim, of course, is the protection of one's reputation.

"Mr Trump has bragged about his non-consensual sexual touching of women. He has bragged about intruding on beauty pageant contestants in their dressing rooms. He acquiesced to a radio host's request to discuss Mr Trump's own daughter as 'a piece of ass'.

"Multiple women not mentioned in our article have publicly come forward to report on Mr Trump's unwanted advances. Nothing in our article has had the slightest effect on the reputation that Mr Trump, through his own words and actions, has already created for himself."

Trump also suggested during his speech on Thursday (13 October) that the mainstream media was rallying around Hillary Clinton.

He said: "Their agenda is to elect Crooked Hillary Clinton at any cost, any price, no matter how many lives they destroy. For them, it is war.

"They will attack you and slander you and seek to destroy your career and family and everything about you, including your reputation. They will lie, lie, lie and do worse than that. Whatever is necessary."