The marble Lincoln statute had green paint on its shins, chair and base, as well as on the floor of the memorial building.
Capt. Steven Booker said the paint spill "appears intentional based off of the splatter." Police were reviewing security camera footage to try to identify possible suspects, he said. No suspects had been identified by Friday afternoon. Officials said they would not release the security footage because the investigation is ongoing.
The memorial will be closed until the National Park Service maintenance crew can clean up the paint, which is expected to happen later Friday.
National Park Service spokeswoman Carol Johnson said the memorial will be returned to the condition it was in before the vandalism.
"It is not permanent damage," she said. "Our historic preservation crew knows exactly what they need to do."
The process of removing the paint was expected to last throughout much of the day, Johnson said.
The memorial, one of the most popular sites on the National Mall, was dedicated in 1922 to the nation's 16th president. The building was designed by Henry Bacon, and Daniel French sculpted the statue of Lincoln. It sits at the opposite end of the National Mall from the Capitol, facing the monument to George Washington.
The memorial has served as a symbol of equality and reunification after the Civil War. It was the site of the Rev. Martin Luther King Jr.'s March on Washington, along with other historic moments.
The Lincoln Memorial is generally open around the clock to visitors. Park rangers leave their posts about 10 p.m. and return about 9 a.m. daily. U.S. Park Police, however, maintain 24-hour patrols at the memorial, said Lt. Pamela Smith.
Lincoln Memorial: http://www.nps.gov/linc
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