By Lauren Fox, CNN

(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 will return to the US Capitol since McCain's death. Senate Minority Leader Chuck Schumer has called for the Senate to rename the Russell Senate Office Building after McCain. 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.