The two were invited by the U.S. Olympic Committee to attend a gala dinner on Wednesday in Washington honoring the 2016 Olympic team and accompany the team to meet President Barack Obama at the White House the following day, Carlos told Reuters on Sunday.
The image of Smith and Carlos, gold and bronze medalists in the 200-meter track event in Mexico City, thrusting their black-gloved fists into the air, has become an enduring symbol of the fight for racial equality.
Their example has surfaced repeatedly in past weeks as an inspiration to African-American National Football League and college players protesting racial injustice after the fatal shootings of several black men by police.
Smith and Carlos paid a high price for their protest, not only with the Olympic Committee but also in the court of public opinion.
"It was against the charter of the Olympic Committee to make a political statement at the victory podium," Carlos said in a phone interview. "But we felt it was the only place we could make the statement at that time."
Standing in black socks, the two Americans bowed their heads and pushed their fists into the air as the U.S. anthem played, shocking the world and many Americans reeling from a turbulent year in the fight for civil rights. They were suspended from the U.S. Olympic team and sent back to the United States.
It was widely interpreted as a black power salute but the athletes later described it as a "human rights salute."
Carlos said he did not expect or want an explicit apology from the Olympic Committee for sending him and Smith home, because their actions were in clear violation of policy. He said, however, that over time and as their raised-fist salute has become a precedent of sorts, U.S. Olympic officials have a better understanding of the reasons behind their protest.
"Time has gone by to the point where they had to take a look at themselves and say, 'These guys weren't bad guys,'" Carlos said. "'They were courageous enough to make a statement for what they believed in.'"
The U.S. Olympic Committee did not return calls requesting comment. The Associated Press reported on Friday that USOC Chief Executive Scott Blackmun had asked Smith and Carlos to serve as ambassadors as the federation tries to bring more diversity to its own ranks.
"I think Tommie and John have played an important and positive role in the evolution of our attitudes about diversity and inclusion, not only in the United States but around the world," Blackmun said.