Washington (CNN) A day after his labor secretary convened a news conference defending himself against accusations of prosecutorial malfeasance, President Donald Trump is questioning whether Alex Acosta's efforts were sufficient in quieting the uproar, people familiar with the matter said.

Trump has remained publicly silent in the 24 hours since Acosta held the question-and-answer session -- at the President's urging -- to defend his role in financier Jeffrey Epstein's plea agreement over sexual assault allegations , which critics have bemoaned as woefully lenient.

Epstein was ultimately sentenced to time behind bars -- but served only 13 months and was allowed to leave for long stretches to work from his office. He avoided a federal trial but did have to register as a sex offender.

Trump, who a day before described Acosta as a "really great" Cabinet member, has privately expressed concern at how the labor secretary's handling of the Epstein case reflects on him and his administration. Trump has not appeared overly concerned with the plea agreement itself, people close to him said.

The President and his aides have been looking at some of the legal commentary since Acosta's performance and are waiting to see how things develop, one White House official said, adding that some in the West Wing want to see whether a review of Acosta's actions reveal any other concerns.

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