Before the service, Mr Trump was also seen shaking hands with former vice president Mike Pence – the first time the pair have been seen in public together since leaving the White House in 2021.
Prior to that, Mr Pence had refused to back Mr Trump’s claim he had won the 2020 election.
Mr Obama and Mr Trump were also seen talking before the service began.
During his eulogy, Mr Biden said Mr Carter taught him the importance of treating “everyone with dignity and respect.”
“To young people, to anyone in search of meaning and purpose, study the power of Jimmy Carter’s example,” the president said. “Character, faith, love – a true patriot.”
Joshua Carter, the former president’s grandson, also said at the service: “He built houses for people who needed homes.
“He eliminated diseases in forgotten places. He waged peace anywhere in the world, wherever he saw a chance. He loved people.”
From 4 January, Mr Carter’s body was carried by a motorcade through Plains, before heading to the Carter Presidential Center in Atlanta.
The former president’s remains were then flown to Maryland and transferred in a ceremony to a hearse, which was carried in a motorcade to the US Navy Memorial in Washington to honour Mr Carter’s service as a lieutenant in the Navy.
He has since been lying in state at the Capitol Building, where the public could pay respects from Tuesday evening through to Thursday morning
Mr Carter’s body will now be returned to his hometown in Georgia for a second service and burial.
There, a private ceremony will be held at Maranatha Baptist Church before another procession through Plains, where supporters are being encouraged to line the streets for the motorcade.
Mr Carter will then be buried on his property next to his late wife, Rosalynn, who died in 2023.