Hamill, 72, who played the powerful Jedi knight Luke Skywalker in the movie series and is a vocal supporter of Biden, took the podium wearing the president's aviator sunglasses.
"I said, 'Mr. President,' and he said, 'You can call me Joe.' And I said, 'Can I call you Joe-bi Wan Kenobi?' He liked that," Hamill joked.
He was referring to Obi-Wan Kenobi, the "Star Wars" character played by Alec Guinness in the original 1977 film, who teaches Skywalker to discover his powers as he battles the dark side of the Force and the sinister Darth Vader.
Hamill described Biden, an 81-year-old Democrat preparing for an almost epic battle with his Republican predecessor Donald Trump in November's US elections, as "the most successful president in my lifetime from a legislative standpoint."
He added that the president showed him photos during a meeting in the Oval Office.
Taking a few questions from reporters - although "no Star Wars questions please" - the actress said she had visited the White House under Democratic presidents Jimmy Carter and Barack Obama, but that "this was really special."
The visit took place on the eve of the so-called Fourth of May, when "Star Wars" fans celebrated by repeating the movie's "May the Force be with you" slogan.
The White House regularly brings guests to press conferences, but these are usually in support of a cause or policy.
South Korean K-pop sensations BTS visited in 2022 to highlight the issue of anti-Asian racism, while US actor Matthew McConaughey took to the podium the same year to promote "gun responsibility" following a massacre at an elementary school in his hometown of Uvalde, Texas.
White House Press Secretary Karine Jean-Pierre said Hamill was "someone who is deeply invested in the direction of this country."
