Washington: Donald Trump could have paid little or even zero income tax in recent years, despite valuing his own worth at more than $US10 billion ($13 billion), experts say.

The Republican presidential nominee has so far refused to release his tax returns even though every other candidate, both Republican and Democrat, has done so for the past 40 years.

As pressure mounted on Mr Trump to make them public, there were growing signs that the Republican Party was nearing breaking point with its nominee - with some insiders admitting they already believe the White House is lost.

It came after a week in which Mr Trump falsely and repeatedly claimed that President Barack Obama was the "founder" of Islamic State, appeared to joke about his Democrat rival Hillary Clinton being assassinated, and contemplated defeat for the first time, saying he would "take a very, very nice long vacation".