Former US Presidents Barack Obama and George W. Bush have voiced concern about the current political climate in the US, urging Americans to reject the politics of "division" and "prejudice" in comments seen as a veiled rebuke of Donald Trump's leadership.

In separate and unrelated appearances, Obama and Bush warned that the US "was being torn apart by ancient hatreds that should have been consigned to history long ago" and called for addressing economic anxiety through common purpose. While not directly addressing Trump, neither left much doubt whom and what they had in mind.

Obama, who has returned to the campaign trail for the first time since leaving the White House, was speaking at a rally in New Jersey on Thursday to support Democratic candidate for Governor Phil Murphy, the New York Times reported. 

"Some of the politics we see now, we thought we'd put that to bed. I mean, that's folks looking 50 years back. It's the 21st century, not the 19th century."

"We are rejecting a politics of division. We are rejecting a politics of fear," Obama said. 

"We are embracing a politics that says everybody counts, a politics that says everybody deserves a chance, a politics that says everybody has dignity and worth -- a politics of hope."

He touched on similar themes at another rally in Richmond, Virginia, saying: "We've got folks who are deliberately trying to make folks angry, to demonise people who have different ideas, to get the base all riled up because it provides a short-term tactical advantage."

Speaking just hours earlier in New York, Bush delivered a speech in which he warned of threats to American democracy and a decay of civic engagement.

Bush offered a blunt assessment of a political system corrupted by "conspiracy theories and outright fabrication" in which nationalism has been "distorted into nativism."

"Bigotry seems emboldened. Our politics seems more vulnerable to conspiracy theories and outright fabrication," Bush said.

"There are some signs that the intensity of support for democracy itself has waned - especially among the young."

Americans, he said, have "seen our discourse degraded by casual cruelty".

While Trump seeks to raise barriers to trade and newcomers, lashing out at targets with relish, Bush defended immigration and free trade, denounced nationalism and bigotry and bemoaned what he called the "casual cruelty" of current public discourse, the Times reported.

"At times it can seem like the forces pulling us apart are stronger than the forces binding us together. We've seen nationalism distorted into nativism, forgotten the dynamism that immigration has always brought to America.

"We see a fading confidence in the value of free markets and international trade, forgetting that conflict, instability and poverty follow in the wake of protectionism. 

"We've seen the return of isolationist sentiments, forgetting that American security is directly threatened by the chaos and despair of distant places," Bush said.

Before his election last year, Trump was highly critical of both Obama and Bush, describing each of them at one time or another as "perhaps the worst President in the history" of the US.

Since his inauguration in January, Trump's combative style and direct public comments on several issues have caused controversy. He has regularly blamed the media, which he says does not focus on his achievements and instead chooses to concentrate on what he describes as "fake news".