They were joined by figures from the American civil rights movement, Jesse Jackson and Congressman John Lewis.
Later, speaking at an environmental conference, the Prince of Wales called on governments and businesses to end the dumping of plastics into the oceans.
Prince Charles and his wife will meet President Barack Obama at the White House on March 19.
The couple – who arrived in Washington DC for their three-day visit on March 17 – were given a guided tour of the Lincoln Memorial sculpture, pausing at the spot where Dr. Martin Luther King gave his famous “I have a dream” speech in 1963.
At Dr King’s nearby memorial, Prince Charles and Camilla met Rev Jesse Jackson and Congressman John Lewis, who helped organize the famous civil rights march in Selma, Alabama, in 1965 – dramatized in the recent movie Selma.
The Prince of Wales and Duchess of Cornwall were also given a tour of Mount Vernon – home of America’s first president, George Washington.
The duchess also paid a visit to Washington’s Shakespeare Theatre Company.
Prince Charles also visited the National Archives, where he viewed the United States’ Charters of Freedom and the 1297 version of the Magna Carta.
He later told leading delegates to an environmental conference on marine waste of his concerns about the “increasing quantity of plastic waste” in oceans.
The prince said he had been “haunted” by images of seabirds found dead after mistakenly eating plastic, and called for better recycling and disposal of plastics.
The solution to problems caused by a “throw-away society” was to move towards a circular economy, where “materials are recovered, recycled and reused instead of created, used and then thrown away”, he said.
The US visit will see also the royals join in commemorating several important milestones.
These include the 150th anniversaries of the end of the American Civil War and the death of President Lincoln, and the 800th anniversary of Magna Carta.
Prince Charles is also expected to receive an award for exceptional leadership in conservation from the International Conservation Caucus Foundation.
Prince Charles and Camilla will also visit the home city of boxer Muhammad Ali, who was born in Louisville, Kentucky.
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