President Barack Obama seemed to inch a little closer on Tuesday to endorsing former Secretary of State Hillary Clinton's presidential bid.

During remarks at a museum dedicated to highlighting the fight for women's equality, the president, who has made clear his admiration for his one-time rival but has not officially endorsed her, said he hoped one day people would be amazed that the United States had not had a female commander-in-chief.

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"I want young girls and boys to come here, 10, 20, 100 years from now, to know that women fought for equality, it was not just given to them," Obama said of the museum.

"I want them to be astonished that there was ever a time when women were vastly outnumbered in the board room or in Congress. That there was ever a time when a woman had never sat in the Oval Office."

Clinton is running against U.S. Sen. Bernie Sanders of Vermont to be the Democratic Party's 2016 presidential candidate. She lost the 2008 race to Obama, who was then a U.S. senator and who later made her the nation's top diplomat in his administration.

Obama, perhaps realizing that people would read his remarks as a hint of support for Clinton, tempered them by saying he did not know when a woman would win the White House.

"I don't know how long it'll take to get there, but I know we're getting closer to that day because of the work of generations of active, committed citizens," he said.

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White House spokesman Josh Earnest said Obama's remarks indicated the country was ready for a woman president, but he stressed the candidates would be judged on their values and policy agenda.

Obama remains hugely popular with the base of Democratic supporters who helped propel him to the White House and re-elect him in 2012. An endorsement of Clinton could help her vanquish Sanders, who is behind the former first lady in amassing the number of delegates needed to become the nominee but has remained a strong challenger with wins in a number of state nominating contests.