The funeral of former US Vice President Dick Cheney, one of the main architects of the Iraq War, took place Thursday in Washington in the presence of the country's political elite, but without Donald Trump, who was not invited because of the mutual enmity between these two Republicans.

"During our years in office together, through the quiet days as well as the toughest, he was everything a president should expect from his second-in-command," said former President George W. Bush at the funeral service at the Washington National Cathedral.

His eight years in the White House, between 2001 and 2009, were spent alongside Dick Cheney as vice president.

"In times of trial, Dick Cheney was a model of focus, vigilance, and composure," added the 43rd President of the United States.

The former Wyoming congressman, who died on November 3 from complications related to pneumonia, was known as a behind-the-scenes figure, working to influence, in particular, US foreign policy. He was recognized as one of the most powerful vice presidents in the country's history.

In an era marked by terrorism, including on US soil, war, and economic changes, this neoconservative will remain known as one of the interventionist "hawks" who played a central and highly controversial role in the decision to invade Iraq in 2003.

As Minister of Defense between 1989 and 1993 under George Bush Sr., he orchestrated Operation Desert Storm against the invasion of Kuwait by Iraqi President Saddam Hussein.

The former vice president was also one of the biggest proponents of enhanced American interrogation techniques, widely considered to be torture.

A staunch Republican, Dick Cheney did not support Donald Trump in the last presidential election, deeming him unfit for the Oval Office. His daughter Liz, a former Republican congresswoman, was one of the few anti-Trump voices within her party.

The current president had not offered any condolences at the time of the announcement of his death.

A White House official told AFP on Thursday that Donald Trump had not been invited to the funeral.

Former President Joe Biden, as well as former Vice Presidents Dan Quayle, Al Gore, Mike Pence and Kamala Harris, were present in the cathedral.

Last year, Donald Trump called Dick Cheney "the king of endless, senseless wars, wasting lives and billions of dollars."