The widow and daughter of John McCain have criticised US President Donald Trump and his online supporters for repeated attacks on the former US senator and Vietnam War hero who was tortured during five- and-a-half years spent as a prisoner of war.

Speaking to employees at an Ohio factory that makes military tanks, Mr Trump again hammered Senator McCain.

"So I have to be honest, I’ve never liked him much," Mr Trump said.

"I really probably never will. But there are certain reasons for it."

Meghan McCain spent the last few days defending her father and politely criticising Mr Trump.

She said the president had reached "a new, bizarre low - attacking someone who is not here is a new low."

She also said, "If I had told my dad ... he would think it is so hilarious that our president was so jealous of him that he was dominating the news cycle in death."

Barely six months after Senator McCain's death, Mr Trump started the latest exchange between himself and the McCain clan on Sunday in a series of tweets, including one that attacked "'last in his class' (Annapolis) John McCain."

Cindy McCain, the senator's widow, sarcastically urged her Twitter followers to "see how kind and loving a stranger can be" and shared with them an online message from someone who described John McCain as a "traitorous piece of warmongering s**t and I'm glad he's dead."

On Tuesday, speaking to reporters in the Oval Office while sitting next the president of Brazil, Mr Trump added: "I never was a fan of John McCain, and I never will be."

The tweets and sound bites triggered a swirl of anti-McCain attacks and pro-McCain appeals on social media, like the one Cindy McCain shared, and cable television discussion.

Without rebuking Mr Trump, Senate Republican leader Mitch McConnell said in a tweet: "Today and every day I miss my good friend John McCain. It was a blessing to serve alongside a rare patriot and genuine American hero in the Senate."

Republican Senator Johnny Isakson was more critical.

In an interview with Georgia Public Broadcasting yesterday, he called Mr Trump's remarks about Senator McCain "deplorable."

The White House had no comment on Mr Trump's latest attacks.

Mr Trump expressed concern yesterday about Senator McCain's role in the handling of a "dossier," compiled before the 2016 US presidential election by a former British spy and paid for by lawyers for the Democratic Party and Hillary Clinton’s presidential campaign.

The dossier alleged Russian financial dealings with Mr Trump and included salacious personal details that remain unconfirmed. 

After the election, a copy of the dossier was given to Senator McCain, who gave it to the FBI, according to court documents that were made public last week.

Mr Trump and his supporters have aggressively attacked the document ever since its contents became public.

"John McCain received a fake and phony dossier ... He got it, and what did he do? He didn’t call me," Mr Trump said during his visit to the Ohio factory.

"He turned it over to the FBI hoping to put me in jeopardy and that’s not the nicest thing to do."

Mr Trump also lashed this week out at a Washington lawyer, a man he claims he barely knows.

He described George Conway as a "whack job" to journalists yesterday.

"A stone cold LOSER," he wrote on Twitter a few hours earlier.

A prominent lawyer in Washington circles but a nobody to ordinary Americans, Mr Conway burst into the public eye because he is married to senior White House aide Kellyanne Conway and has begun loudly questioning Mr Trump's mental stability on Twitter.

The Twitter president has largely dispensed with formal news briefings, finding that a tweet alone can get everyone talking - without giving them much chance for questioning.

He defended this method of communication as an antidote to what he calls the "corrupt" and "fake" media. By that, he means most standard news organisations.

"It's a way that I can get honesty out," he said.

It is a way where Trump typically gets to punch first and punch hard, thereby dominating the news agenda.

Mr Conway, however, has broken the mold and leveraging his position as husband to a Trump aide, posting outrage-seeking tweets that claim to diagnose personality disorders, he has effectively out-trolled the troller in chief.

With Mr Trump soon starting his 2020 reelection campaign and Democrats launching their own nomination battle, the ugly back and forth is set to intensify.

But Mark Rom, a politics professor at Georgetown University, predicted that Democratic candidates will get surrogates to do the dirty work while they try to keep above it all.

Their mantra, he said, will be modelled on the icily dismissive approach taken by the House of Representatives speaker, Nancy Pelosi: "I'll just ignore that little man."