"We met with contractors today, will probably be forced to release and drain much of the water in order to do the necessary repairs, but will have them done as quickly as possible," Trump wrote in a post on the social media website Truth Social.
Several alleged vandals have been arrested, according to Trump.
"Many additional people have been arrested having to do with the disgraceful Vandalism of our beautiful Reflecting Pool," he wrote.
One man arrested was David Hearn, 67, who owned a company that made composite used to build watercraft. He said he stopped by the pool during a bike ride on Friday to see what was going on.
Hearn, a former Olympic canoe racer, told The Associated Press that he wanted to examine the peeling new coating. He said he briefly touched a chunk that was still attached to the side of the pool, then let go shortly after a park worker told him to.
But, Hearn said, he was then detained by National Guard troops and Park Police for five hours before being released on Friday night.
"I'm a curious citizen," Hearn said in a telephone interview.
"I reached down to see what it felt like. It was very rubbery."
Trump did not provide evidence to support his allegation of vandalism, which he said included someone pouring corrosive chemicals into the pool.
Trump said his predecessors had let the pool turn an algae-stained green and that he'd line it with "American flag blue" so it better reflected the Washington Monument.
But after the new pool was unveiled, its blue tinge quickly became a familiar green. Workers treated it with chemicals to kill the algae, but then the painted blue lining on the bottom began to peel.
Trump announced on June 6 that work was completed on a $US14.7 million ($A21 million) renovation project for the pool.
Soon after, workers started pouring hydrogen peroxide into the pool to combat an algae bloom that had turned it green, instead of the expected dark blue.
Earlier this week, the paint on the reflecting pool was peeling away from the bottom and into the algae-tinted water.
The pool renovation is part of Trump's plans to remake the US capital city, which include tearing down the East Wing of the White House for a new ballroom and building a massive arch near Arlington National Cemetery where the US honours the nation's war dead and other prominent Americans.
