It was not immediately clear what Kudlow's condition was.
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Kudlow, a Republican who served as an economic adviser to former President Ronald Reagan in the 1980s and also worked on Wall Street, is an ardent advocate of "supply side" economic policies that focus on cutting taxes and reducing regulations.
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Mr. Kudlow is nominally in favour of free trade, but has backed Mr. Trump's nationalistic economic agenda, which has included steel and aluminium tariffs against Canada, Mexico and the European Union, as well as threats of further tariffs on autos.
"He is now in Walter Reed Medical Center", Trump added.
Kudlow joined the president at the Group of Seven summit in Quebec on Friday and Saturday. As recently as Sunday, he had appeared on TV defending the president's attacks on Canadian Prime Minister Justin Trudeau, saying that Trudeau had committed a "betrayal".
Trump's choice of Kudlow to be his top economic aide elevated the influence of a longtime fixture on the business news network CNBC.