President Trump's initial absence at his wife's side did not go unnoticed on Twitter

President Trump‘s West Wing may gush leaks, but First Lady Melania Trump‘s Monday-morning hospitalization for a procedure to treat an unspecified “benign kidney condition” was kept secret by her East Wing staff until an announcement by email at 3:11 p.m. ET.

The president remained at the White House throughout, with two meetings on his public schedule for Monday: his daily intelligence briefing in the Oval Office at 11 a.m. and then, at 12:30 p.m. in his private dining room, lunch with Vice President Mike Pence.

According to the White House, Trump’s Monday schedule also included phone calls to Prime Minister Justin Trudeau of Canada, President Mauricio Macri of Argentina, and James Shaw, Jr., the hero who disarmed a gunman in a Tennessee Waffle House last month.

After tweeting twice on Monday afternoon — about trade and his “personal relationship with President Xi” of China, and then about “fake news” — he boarded Marine One shortly after 5 p.m. for the trip to Walter Reed National Military Medical Center, where his wife was expected to remain hospitalized “for the duration of the week,” her spokeswoman said.

“Heading over to Walter Reed Medical Center to see our great First Lady, Melania. Successful procedure, she is in good spirits,” Trump tweeted. “Thank you to all of the well-wishers!”

Only minutes earlier, he was evidently focused on the latest damaging leaks out of the West Wing. There has been a firestorm of controversy since it was leaked last week that White House special assistant Kelly Sadler reportedly joked in a private staff meeting about Sen. John McCain’s brain cancer, saying his vote in the Senate “doesn’t matter, he’s dying anyway.”

The president’s initial absence at his wife’s side did not go unnoticed by Twitter users including author Amy Siskind, president of women’s rights organization The New Agenda, who fired off a sarcastic tweet about the president’s “busy” schedule.

The president’s helicopter touched down at Walter Reed at 5:18 p.m. ET, according to a pool report.

Mrs. Trump’s spokesperson, Stephanie Grisham, told PEOPLE in a statement that the first lady “is in good spirits.”

And Grisham told a press pool gathered at Walter Reed: “The first lady is in good spirits and doing quite well.”

Melania and Donald Trump

According to CNN, the spokeswoman also said that the president phoned Mrs. Trump — “and they spoke extensively” — before her procedure; and he later spoke with her doctor.

The president spent over an hour at the hospital visiting his wife, according to a pool report.

The presidential motorcade departed Walter Reed just before 6:30 p.m. ET, under stormy conditions, to head back to the White House.

It is not unprecedented for a first lady to undergo a surgical procedure without the president on stand-by in the waiting room. When Laura Bush underwent surgery in September 2007 to relieve pain from pinched nerves in her neck, then-President George W. Bush was in Australia for an APEC summit. Bush phoned his wife from his trip to check on her.

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Meanwhile on Monday afternoon, as the American public reacted with surprise and concern to the first lady’s hospitalization, friends of the first couple were also taken off guard by the news.

Paolo Zampolli, a UN ambassador and a longtime friend of Melania and Donald Trump’s, tells PEOPLE that after he learned of Mrs. Trump’s surgery from the breaking news, “I sent her a friendly text message, that our prayers, love and thoughts are with her and wish her a speedy recovery.”

Another friend of the first couple also tells PEOPLE: “I have heard nothing about this. The first I knew was when I saw it on the news!”

A third source close to the Trump family was also shocked and knew nothing of any symptoms the first lady may have had.

“I had absolutely no clue this was going on,” the source close to the family tells PEOPLE.

  • With reporting by DIANE HERBST and LINDA MARX