Rick Davis, former presidential campaign manager for McCain who is serving as a family spokesman, read the farewell message Monday at a press briefing in Phoenix.
In the statement, McCain reflected on the privilege of serving his country and said he tried to do so honorably. He also touched on today's politics.
"Do not despair of our present difficulties but believe always in the promise and greatness of America, because nothing is inevitable here," McCain wrote. "Americans never quit. We never surrender. We never hide from history. We make history."
McCain died Saturday from an aggressive form of brain cancer. Plans taking shape called for McCain to lie in state Wednesday in the Arizona State Capitol on what would have been his 82nd birthday. A funeral will be conducted Thursday at North Phoenix Baptist Church with former Vice President Joe Biden speaking.
In Washington, McCain will lie in state Friday in the Capitol Rotunda with a formal ceremony and time for the public to pay respects. On Saturday, a procession will pass the Vietnam Veterans Memorial and arrive for a funeral at Washington National Cathedral. Former Presidents George W. Bush and Barack Obama are expected to speak at the service.
The Senate has draped John McCain's desk in black fabric and placed a vase of white roses on top. Monday was the Senate's first day back in session since his death, though McCain had not been back to Washington since December.
A private funeral is planned for Sunday afternoon at the Naval Academy Chapel followed by a private burial at the academy cemetery.
President Donald Trump was not expected to attend any of the services.
McCain was a noted critic of Trump, and Trump's response to McCain's death has been closely watched.
The flag atop the White House flew at half-staff over the weekend in recognition of McCain's death but was raised Monday and then lowered again amid criticism.
Trump said Monday afternoon that he respects the senator's "service to our country" and signed a proclamation to fly the U.S. flag at half-staff until his burial.
When asked about Trump's response to McCain's death after the flag was raised Monday, Davis said that the family is focusing on the outpouring of support from around the world instead of "what one person has done or said."
"The entire focus of the McCain family is on John McCain," Davis said. "There really is no room in the McCain family today to focus on anything but him."
In Arizona, high-profile campaigns announced that they have suspended some activity this week.
McCain was just one of 11 U.S. senators in the state's 116-year history, and on Tuesday, primary voters will decide the nominees in races across all levels of government. There's also the sensitive question of who will succeed McCain.
Arizona law requires the governor of the state to name an appointee of the same political party who will serve until the next general election. Since the time to qualify for November's election is past, the election would take place in 2020, with the winner filling out the remainder of McCain term until 2022.
Possible appointees whose names circulate among Arizona politicos include McCain's widow, Cindy McCain, former U.S. Senator Jon Kyl and Republican Gov. Doug Ducey's chief of staff Kirk Adams.
Throughout the weekend, Arizona politicos across all levels of government offered remembrances of McCain. Noting McCain's death, several candidates, including Democratic Rep. Kyrsten Sinema and Republican Rep. Martha McSally, who are expected to win their party's races for the state's other U.S. Senate seat, on Sunday evening said they would suspend their campaigns on Wednesday and Thursday. Ducey, whose office is coordinating services at the Arizona State Capitol for McCain, will not attend any campaign events between now and when McCain is buried.
Tributes poured in from around the globe. French President Emmanuel Macron tweeted in English that McCain "was a true American hero. He devoted his entire life to his country." Israel's prime minister, Benjamin Netanyahu, said McCain's support for the Jewish state "never wavered. It sprang from his belief in democracy and freedom." And Germany's chancellor, Angela Merkel, called McCain "a tireless fighter for a strong trans-Atlantic alliance. His significance went well beyond his own country."
McCain was the son and grandson of admirals and followed them to the U.S. Naval Academy. A pilot, he was shot down over Vietnam and held as a prisoner of war for more than five years. He went on to win a seat in the House and in 1986, the Senate, where he served for the rest of his life.
"He had a joy about politics and a love for his country that was unmatched," Sen. Amy Klobuchar, D-Minn., told CNN's "State of the Union." ''And while he never made it to the presidency, in the Senate, he was the leader that would see a hot spot in the world and just say, we need to go there and stand up for that democracy."
Gov. Rick Snyder lowers flags in honor of U.S. Sen. John McCain
Gov. Rick Snyder has ordered U.S. and Michigan flags to be lowered to half-staff Wednesday, Aug. 29 through Sunday, Sept. 2, on all state buildings and within the state Capitol complex in honor of U.S. Sen. John McCain, who died Saturday, Aug. 25. The flags will be lowered beginning Wednesday with a public viewing in Arizona, until Sunday when he will be laid to rest following a private service in Maryland.
“Sen. John McCain made an incredible, positive impact on our country and on all who call it home. He was a hero and public servant who worked each and every day to make this country better. Sen. McCain will be remembered for his service to the American people, both as an elected official and a military member,” Snyder said. “Sue and I send our deepest condolences to Sen. McCain’s loved ones during this trying time. It is my hope that we will come together as a nation and honor his legacy.”
“Sen. John McCain was an American hero. He lived an impactful life that set the standard for selflessness, sacrifice and grace. Surely his legacy of service will live on,” Lt. Gov. Brian Calley said.
McCain served in the U.S. Navy as a Navy fighter pilot, where he endured nearly six years as a prisoner of war in North Vietnam. In 1986, he ran for his first term as a U.S. Senator, a position he held until his death.
Public viewings will be held in his honor Wednesday, Aug. 29 at the Arizona State Capitol and Friday, Aug. 31 in the rotunda of the U.S. Capitol.
This flag order is in accordance with Executive Order 2013-10. Michigan residents, businesses, schools, local governments and other organizations are encouraged to display the flag at half-staff. Flags should be returned to full staff on Monday, Sept. 3.
When flown at half-staff or half-mast, the U.S. flag should be hoisted first to the peak for an instant and then lowered to the half-staff or half-mast position. The flag should again be raised to the peak before it is lowered for the day.