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Trump wrote on Twitter on Sunday that "now they have left Canada for the US, however, the US will not pay for their security protection. They must pay!"
In January this year, Harry and Meghan said they would step away from their royal duties.
A spokeswoman for the couple said in a statement: "The Duke and Duchess of Sussex have no plans to ask the US government for security resources. Privately funded security arrangements have been made."
Meghan Markle, who married Prince Harry, the grandson of Queen Elizabeth, in 2018, criticised Trump during his 2016 election campaign as misogynistic and divisive.
Last year, Trump, on being told of Meghan’s criticism, said: "I didn’t know that. What can I say? I didn’t know that she was nasty." But he also wished her well in her new life as a British royal.
Britain's Sun newspaper reported last week that Harry and Meghan took a private flight to Los Angeles, but did not say when.
Earlier this month, the United States and Canada agreed to close their border to non-essential travel at land crossings to ease the strain on health systems caused by the coronavirus.
The couple had been living for several months with their son, Archie, on Vancouver Island in Canada.
Meghan was raised in the Los Angeles area and her mother, Doria, still lives there.
Walt Disney Co said last week that Meghan had narrated a nature documentary that will be released on its Disney+ streaming platform on Friday.
Last month, Canada said it would no longer provide security once the couple were no longer working members of the British royal family.
The Royal Canadian Mounted Police had been assisting London’s Metropolitan Police with security for the couple "intermittently" since November, when they began a six-week vacation in Canada, Reuters reported in February.
The couple stunned the royal family in early January with an announcement they would be stepping down from their roles as senior royals, in order to gain freedom from the intense media scrutiny that has followed them for several years.