US President Donald Trump has rejected media allegations that he belittled slain American service members by referring to them as "losers" and "suckers".

An article published in The Atlantic on September 3, quoting anonymous sources, claimed Trump made the remarks when he visited France in 2018, Xinhua news agency reported.

During the visit, the President had cancelled a trip to a French cemetery where American soldiers killed in the World War I were buried.

"Only an animal would say that," Trump said at a press conference in the White House on Monday.

He added that the article's author, The Atlantic's Editor-in-Chief Jeffrey Goldberg, is pro-Democrat and has a "tremendously bad history".

"He (Goldberg) made up the story, it's a totally made-up story," Trump said.

On Sunday, Goldberg said the article was just the tip of the iceberg.

"I would fully expect more reporting to come out about this and more confirmation and new pieces of information in the coming days and weeks," Goldberg told CNN on Sunday.

CNN has confirmed several aspects of The Atlantic's reporting, also with sources who chose to remain anonymous.

Trump has previously described Goldberg as a "slimeball" and called for the firing of a Fox News reporter who also confirmed some details of the article.

The latest Military Times poll, conducted before the Democratic and Republican conventions as well as The Atlantic's reporting, showed a steady decline in troops' opinion of Trump since his election four years ago.

Among active-duty service members surveyed in the poll, 41 per cent said they would vote for Joe Biden, the Democratic nominee, while 37 per cent said they plan to vote to re-elect Trump.

In a poll conducted at the start of Trump's presidency, 46 per cent of troops had a favourable view of him, versus 37 per cent who had an unfavourable opinion, according to a Military Times report.