"I encourage everyone who chooses to be negative (and) question my work at the @WhiteHouse to take time and contribute something good (and) productive in their own communities," Trump tweeted Saturday.
As of Saturday morning, there are at least 335 reported cases and 17 deaths in the US, according to CNN's latest count.
The first lady's office did not return CNN's requests for comment.
On Thursday, Melania Trump posted about the construction status on the tennis pavilion, with pictures of her wearing a hard hat and looking over what appear to be architectural plans.
The private pavilion will be located on the South Lawn of the White House and serve as a "place to gather and spend leisure time for First Families."