Washington CNN  — 

Republican Sen. John McCain had one more message for his fellow Americans.

In a letter read by longtime aide Rick Davis on Monday, McCain encouraged Americans to unite around the ideals that connect them rather than focus on divisions. He also pointedly asked Americans to tear down walls rather than build them.

“We weaken our greatness when we confuse our patriotism with tribal rivalries that have sown resentment and hatred and violence in all the corners of the globe,” Davis read from McCain’s letter. “We weaken it when we hide behind walls, rather than tear them down, when we doubt the power of our ideals, rather than trust them to be the great force for change they have always been.”

In his letter, McCain noted he had lived a “rewarding life,” full of friendships and love, adventure and even at times extraordinary hardship that he wouldn’t trade.

“I have tried to serve our country honorably. I’ve made mistakes, but I hope my love for America will be weighed favorably against them,” McCain’s letter read. “I have often observed that I am the luckiest person on earth. I feel that way even now as I prepare for the end of my life. I have loved my life, all of it. I have had experiences, adventures and friendships enough for 10 satisfying lives, and I am so thankful. Like most people, I have regrets. But I would not trade a day of my life, in good or bad times, for the best day of anyone else’s. “

As the remembrances of McCain continue in the senator’s home state of Arizona, Monday marks the first day that lawmakers returned to the US Capitol since McCain’s death. As is customary, McCain’s Senate desk was draped in a black cloth. Atop the desk sat a vase of white roses.

Senate Majority Leader Mitch McConnell devoted his entire opening remarks Monday afternoon to McCain.

“I think it’s fair to say the passion that John brought to his work was unsurpassed in this body. In more than 30 years as a senator, he never failed to marshal a razor-sharp wit, a big heart and a fiery spirit,” McConnell said. “When John saw an issue the same way you did, you knew you’d just found your most stalwart ally. You’d thank your lucky stars. Because when you found yourself on the other side of that table, as I think all of us learned, you were in for a different kind of unforgettable experience.”

McConnell recounted a visit earlier this year to Sedona, Arizona, to see McCain, recalling how the two men – both fierce and loyal tacticians of the Senate – had the privilege to reminisce about their time in the body together.

“John did things his way these last months,” McConnell said. “So, John McCain has fought his last battles and cast his final votes. But the nation he loved is still not done with him yet.”

McConnell said that this week McConnell would lie in state at the Capitol.

“As the days turn to weeks, I know we’re all eager to come together and collaborate on ways we can continue to honor his memory,” McConnell said. “Generation after generation of Americans will hear about the cocky pilot who barely scraped through Annapolis, but then defended our nation in the skies. Witnessed to our highest values even through terrible torture. Captured the country’s imagination through national campaigns that spotlighted many of our highest values and became so integral to the United States Senate, where our nation airs and advances its great debates.”

Senate Minority Leader Chuck Schumer has called for the Senate to rename the Russell Senate Office Building after McCain.

As he left the Senate floor following his tribute to McCain, McConnell was asked for his thoughts on the proposal.

“We’ll be talking about the best ways to honor Sen. McCain in the days ahead,” he said, sidestepping the issue. Asked directly if he supports or opposes the idea, he declined to respond and walked silently into his office.

During his opening remarks Monday, Schumer described a friendship with McCain that evolved slowly and culminated in a massive immigration reform bill that passed the Senate in 2013.

“He was unafraid to take on his party,” Schumer said. “He could put the temper in temperament, He was a brave and honest man.”

Over the weekend, senators remembered their colleague and friend. Sen. Jeff Flake, the junior senator from Arizona, appeared on CNN Sunday and emotionally remembered his mentor.

“It’s tough to imagine politics without John McCain. But we need to go on,” Flake said.

Sen. Susan Collins, a Republican from Maine, said she would deeply miss McCain’s humor and guidance.

“I am going to miss the fact that he was so much fun,” Collins said.

CNN’s Ted Barrett contributed to this report.