Jimmy Carter brought a fleeting moment of national unity to a divided America on Thursday as all five living US presidents gathered for their predecessor's moving state funeral in Washington's National Cathedral.

At the rare gathering just days before Donald Trump's return to the White House, sitting President Joe Biden gave a eulogy describing "character" as fellow Democrat Carter's main attribute.

Trump shook hands with former president Barack Obama on the country's day of mourning, while Bill Clinton and George W Bush were also there to pay their respects.

But Biden, 82, also appeared to deliver a veiled swipe at Trump, the Republican whose racially-charged rhetoric and efforts to overturn the 2020 election he has often criticised as threats to democracy.

"We have an obligation to give hate no safe harbour," said Biden, also stressing the importance standing up against "the greatest sin of all, the abuse of power."

After the speech, Biden briefly tapped the flag-draped coffin of Carter, America's 39th commander-in-chief, who died on December 29 at the age of 100 in his native Georgia.

The presidential funeral was the first since George H W Bush died in 2018.

During the service, family members and former political adversaries alike paid emotional tributes to Carter, the oldest-ever former US president and the only one to make it to three figures.

Carter's coffin was earlier transported by an honour guard from the US Capitol, where thousands of mourners had paid their respects as the former president lay in state.

Thursday has been designated a national day of mourning in the United States with federal offices closed. (AFP)