After the death of the man he beat for the White House, Bill Clinton remembered a famous letter left in the Oval Office and said: “I just loved him.”

George HW Bush, the Republican 41st president, died on Friday night in Texas at the age of 94. He left his note for the Democratic 42nd president on 20 January 1993.

“Dear Bill,” he began. “When I walked into this office just now I felt the same sense of wonder and respect that I felt four years ago. I know you will feel that, too.”

Presidents traditionally leave such letters. But Bush’s note to Clinton has taken on greater popular significance since January 2017 when Donald Trump, the 45th president, succeeded the 44th, Barack Obama.

When the two met at the White House, they were stiffly formal. Obama’s letter to Trump followed suit. In office, Trump has devoted himself to undoing Obama’s legacy. In return, Obama has involved himself in the political fight to a greater extent than usual.

“I wish you great happiness here,” Bush wrote in his letter to Clinton, with a warmth that might now seem as from another world.

“I never felt the loneliness some presidents have described. There will be very tough times, made even more difficult by criticism you may not think is fair. I’m not a very good one to give advice; but just don’t let the critics discourage you or push you off course.

Underlining “our”, he added: “You will be our president when you read this note. I wish you well. I wish your family well. Your success now is our country’s success. I am rooting hard for you.

“Good Luck, George.”

Writing in the Washington Post, Bill Clinton said Bush’s words showed “natural humanity”. He added that while his friendship with Bush was at first “respectful”, it was after they became involved in relief efforts for the 2004 Indian Ocean tsunami and Hurricane Katrina in 2005 that the relationship blossomed.

“His friendship has been one of the great gifts of my life,” Clinton said. “I cherished every opportunity I had to learn and laugh with him.”

He added: “Given what politics looks like in America and around the world today, it’s easy to sigh and say George HW Bush belonged to an era that is gone and never coming back – where our opponents are not our enemies, where we are open to different ideas and changing our minds, where facts matter and where our devotion to our children’s future leads to honest compromise and shared progress.

“I know what he would say: ‘Nonsense. It’s your duty to get that America back.’”

Clinton’s wife lost the 2016 presidential election to Trump, who has constantly called for her to be imprisoned. In an Instagram post on Saturday, she said the letter reminded her of a gentler time. It made her cry when she first read it, Hillary Clinton wrote, and did so again when she heard Bush was dead.

Obama was one of Bush’s last visitors in Houston this week. Jimmy Carter, the 39th president, said in a statement Bush’s presidency was “marked by grace, civility, and social conscience”.

Quoting James Baker, Bush’s secretary of state, the New York Times reported that the 41st president’s last words were spoken to the 43rd, his son George W Bush.

“I love you too,” Bush Sr was quoted as saying.