Mrs Trump made her worldwide debut as first lady at last year's G7 summit in Italy, and went on to attend the G20 in Germany.
It's the second year the Trumps have opened the White House to Gold Star families.
The first lady stayed behind Friday when President Donald Trump, his daughters, eldest son and son-in-law went to the Camp David retreat for the weekend. Melania announced the new initiative on May 7, right before she made herself scarce. "She just looked so lovely".
"I see the media is working overtime speculating where I am & what I'm doing", Melania tweeted on Wednesday.
On May 10, the first couple welcomed home American hostages from North Korea. But Melania Trump's unusual 25-day absence from public view following surgery for a "benign" kidney condition has raised questions.
Videos of the first lady at the event, which marked her first public appearance in more than three weeks after undergoing a kidney procedure at Walter Reed National Military Medical Center, were quickly posted on social media. Mrs. Truman also spent a lot of time in Missouri with her mother.
The White House has given few details of the condition but has said it was "benign".
Denmark bans niqabs and burqas in public areas
Those violating the ban will be forced to pay 1,000 kroner (£118; $157), with fines ten times higher for repeat offenders. Justice Minister Soren Pape Poulsen in April said the Danish police will not forcibly remove veils from women.
The president literally pointed at a window, indicating the presence of the first lady, but ... she wasn't there.
We'll have to wait until tonight to hear if she really shows up.
White House silence about her subsequent absence from public appearances with the president stoked conspiracy theories, and Rolling Stone's Jamil Smith came out with another one on Sunday.
Grisham said earlier that the first lady has been meeting with staff and working on projects.
Melania Trump won't be joining her husband at the 2018 G7 summit in Quebec or accompanying him to the meeting planned with North Korea's leader in Singapore following the G7.
The first lady's lack of recent viewings, prior to Monday's event, has created a storm of "where is she?" memes on the internet, and speculation on her whereabouts ran the gamut, from New York City to Palm Beach.
Her absence sparked all kinds of wild speculation, but the first lady has shown no interest in making an appearance just to knock down rumors. The event, however, will be "closed press", meaning that the media will not be allowed inside, allowing Melania to mostly remain out of the spotlight.