John McCain's daughter has said her father embodied "American greatness" as she used his funeral to dismiss "cheap rhetoric" in a pointed rebuke of Donald Trump.

As the president enjoyed a round of golf after a week dominated by the death of one of his most prominent Republican critics, Meghan McCain took a swipe at him during a heartfelt eulogy, the Daily Telegraph UK reports.

Speaking at times through tears about her father, the former Arizona senator and presidential candidate, Ms McCain said: "The America of John McCain has no reason to be great again because America was always great."

Ms McCain did not mention Trump by name but it was clear that her comment - which was greeted with applause by those at the Washington National Cathedral - was directed at the Oval Office.

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Elsewhere during the two-and-a-half hour service the US president, who was not invited, and his approach to politics appeared to be critiqued by Barack Obama among others.

One of three former presidents in attendance, Obama warned of how modern politics was dominated by "bombast and insult and phony controversies" before urging Americans to live by McCain's principles of patriotism.

George W Bush, the former Republican president who also gave a eulogy, said McCain recognised "his opponents were still patriots and human beings".

Henry Kissinger, one of America's best known former diplomats, praised the former senator for warning against America's "withdrawal from the world".

The family of Senator John McCain from left, Jimmy McCain, Cindy McCain, Ben Domenech and his wife Meghan McCain, and Jack McCain watch as the casket is placed into the hearse. Photo / AP
The family of Senator John McCain from left, Jimmy McCain, Cindy McCain, Ben Domenech and his wife Meghan McCain, and Jack McCain watch as the casket is placed into the hearse. Photo / AP

Trump, who clashed frequently with McCain in recent years despite both men being from the same political party, spent the morning issuing familiar attacks on Twitter.

As the body of McCain was being processed through Washington DC in a coffin draped in the American flag, Trump was tweeting criticism of his own law officials from inside the White House.

Around half an hour into the service, which was broadcast live on cable news channels, Trump left the White House in a 'Make America Great Again' hat and short-sleeved shirt, heading for one of his golf clubs.

The day epitomised a political struggle inside the Republican Party which McCain, a war hero and six-term senator, and Trump, a reality TV star turned elected president, had come to embody in recent years.

Trump once mocked McCain's time as a prisoner of war in Vietnam, joking: "I like people that weren't captured." McCain last year voted against Mr Trump's attempt to repeal the healthcare legislation dubbed 'Obamacare', leading to its defeat.

At the funeral of McCain, who died aged 81 of brain cancer and has been mourned in public ceremonies for much of this week, were many leading figures of the Washington establishment from both sides of the aisle.

Family and friends watch as the casket arrives for a memorial service for Senator John McCain at Washington National Cathedral in Washington. Photo / AP
Family and friends watch as the casket arrives for a memorial service for Senator John McCain at Washington National Cathedral in Washington. Photo / AP

Obama and Bush were joined by Bill and Hillary Clinton on the front row of the cathedral. Mitch McConnell and Chuck Schumer, the Republican and Democrat leaders in the US Senate, sat together in a sign of bipartisanship.

Top Trump administration figures were also there including Ivanka Trump and her husband Jared Kushner, White House chief of staff John Kelly and US defence secretary Jim Mattis. But Trump, overlooked for an invite, was not.

Ms McCain, 33, made clear her views of the US president during her address. "We gather here to mourn the passing of American greatness," she said.

"The real thing, not cheap rhetoric from men who will never come near the sacrifice he gave so willingly, nor the opportunistic appropriation of those who lived lives of comfort and privilege while he suffered and served."

Obama, who has not often criticised his predecessor, also appeared to have Trump in mind as he issued a critique of today's political debate.

"So much of our politics, our public life, our public discourse can seem small and mean and petty, trafficking in bombast and insult and phony controversies and manufactured outrage," Obama said.

Former President Barack Obama pauses as he speaks at a memorial service for Senator John McCain at Washington National Cathedral in Washington. Photo / AP
Former President Barack Obama pauses as he speaks at a memorial service for Senator John McCain at Washington National Cathedral in Washington. Photo / AP

"It's a politics that pretends to be brave and tough but in fact is born in fear. John called on us to be bigger than that. He called on us to be better than that."

There were lighter moments during the ceremony as former presidents remembered McCain's quirks and flaws as well as his bravery.

Obama and Bush, who beat McCain in the 2008 US election and the 2000 race for the Republican presidential nomination respectively, had been picked personally by the former Arizona senator to give eulogies.

Obama said the decision reflected McCain's irreverence and sense of humour, saying: "What better way to get the last laugh than to make George and I say nice things about him to a national audience."

Obama also joked about McCain's temper, saying: "When it flared up, it was a force of nature, a wonder to behold. His jaw grinding, his face reddening, his eyes boring a hole right through you - not that I ever experienced it firsthand, mind you."

Former President George W. Bush speaks at a memorial service for Senator John McCain at Washington National Cathedral in Washington. Photo / AP
Former President George W. Bush speaks at a memorial service for Senator John McCain at Washington National Cathedral in Washington. Photo / AP

But he also paid tribute to McCain's belief in American values: "John understood, as JFK understood, as Ronald Reagan understood, that part of what makes our country great is that our membership is based not on our bloodline, not on what we look like, what our last names are, it's not based on where our parents or grandparents came from, or how recently they arrived, but on adherence to a common creed: that all of us are created equal, endowed by our creator with certain inalienable rights."

Bush recalled McCain as a champion for the "forgotten people" at home and abroad. He said: "John's voice will always come as a whisper over our shoulder - we are better than this, America is better than this."

Earlier in the day a coffin draped in the American flag bearing McCain's body, which had been lying in state at the US Capitol, was processed through Washington DC.

The family of Senator John McCain follows as his casket is carried during the recessional at the end of a memorial service at Washington National Cathedral in Washington. Photo / AP
The family of Senator John McCain follows as his casket is carried during the recessional at the end of a memorial service at Washington National Cathedral in Washington. Photo / AP

The procession stopped at a memorial for the Vietnam War, which Mr McCain served in and eventually held capture as a prisoner of war for six years.

McCain's widow Cindy laid a wreath at the memorial alongside Kelly and Mattis. She paused and clasped her fingers in what looked like a moment of prayer.