In Washington, flags on Capitol Hill and the White House were lowered to half-mast in his honor.
The Republican Senator and Vietnam War fighter pilot has died at the age of 81.
Sen. John McCain's service to his country began more than six decades ago at the U.S. Naval Academy at Annapolis and will end there in a cemetery overlooking Maryland's Severn River.
McCain said of Trump's comments: "No prior president has ever abased himself more abjectly before a tyrant".
Ward acknowledged that she and McCain, whom she had challenged in the 2016 Republican primary, "held different political views on many, many things - on domestic policy, foreign policy, and of course, on President Trump".
During President Barack Obama's time in office, four sitting senators died: Ted Kennedy, D-Mass., in 2009; Robert Byrd, D-W.Va., in 2010; Daniel Inouye, D-Hawaii, in 2012; and Frank Lautenberg, D-N.J., in 2013.
Friday morning, lawmakers will gather in the Rotunda to salute McCain; a funeral service will be held Saturday at Washington's National Cathedral.
McCain frequently battled with Trump and his family has said he did not want the president to attend his funeral.
Media reports earlier this year said the senator had expressly asked that President Donald Trump not be invited.
"This is a rare and distinct occurrence for a truly special man", said Arizona Governor Doug Ducey, adding: "John McCain is Arizona". French President Emmanuel Macron tweeted in English that McCain "was a true American hero".
Lawmakers and residents in western CT paused to remember Arizona Sen. On Saturday, his grave was marked where he had written he wanted to be buried - next to his best friend from his Naval Academy days, Adm.
Former presidents George W. Bush, a Republican, and Barack Obama, a Democrat - his successful rivals in, respectively, the 2000 and 2008 elections - are set to speak at the national memorial service, according to The New York Times.
"I think it should be a conservative, someone that supports President Trump - I think that should be the main issue", said Joe Arpaio, the former county sheriff whom Trump pardoned past year and who is currently running for the seat now held by Flake, who is not seeking re-election. "But I'd hope that whoever goes in there would have same dedication to country over party that John McCain always had".
Carrazco said that he served two tours in Vietnam, as long as McCain was war prisoner. "The nation mourns the loss of a great American patriot, a statesman who put his country first and enriched this institution through many years of service", said Senate Majority Leader Mitch McConnell, R-Ky. Meghan McCain fired back in a tweet that Trump's attacks on her father "never stops being gross". May we be responsible enough to heed to his plea, wise enough to follow his example, and fortunate enough to have a career in service as long and accomplished as his.
I will remember Senator John McCain as a champion for people around the world struggling for their right to be heard, and willing to risk everything for the freedoms and the democratic values that America represents to them.
Trump's references to McCain in recent months were confined to contempt-filled moments at his political rallies when he would mimic the thumbs-down signal the senator had made when he voted against repealing the Affordable Care Act.