The astronaut Peggy Whitson, who early Monday surpassed the 534-day record for most time in space by an American, received a congratulatory call about nine hours later from President Trump and his daughter Ivanka.

President Trump called the International Space Station from the Oval Office, congratulated Dr. Whitson and urged NASA to go further, even saying — perhaps jokingly — that he would like to send an American to Mars “during my first term or at worst during my second term.”

Dr. Whitson had specified that a bill signed by Mr. Trump in March authorizing $19.5 billion in funding for NASA directed the agency to send astronauts to the planet during the 2030s. But the president, undeterred, said later in the call that such a mission could take place “a lot sooner than we’re even thinking.”

At 1:27 a.m. Eastern, Dr. Whitson, 57, surpassed a record previously held by the astronaut Jeff Williams, who spent 534 cumulative days in space. Her current mission launched in November, and though it originally was scheduled to return home in June, it is now scheduled to last until September.