"Smart!" a post on Trump's official Facebook page said Thursday, linking to a report on Jordanian news website Al Bawaba which alleged that Kuwait had "mirrored" a decision by the Trump administration to temporarily bar travelers from several countries.
The article alleged that "Syrians, Iraqis, Iranians, Pakistanis and Afghans" would not be allowed to enter the Persian Gulf state "while the blanket ban is in place".
But Kuwait's foreign ministry refuted the report, which was widely picked up by news websites popular with Trump supporters.
Kuwait "categorically denies these claims and affirms that these reported nationalities ... have big communities in Kuwait and enjoy full rights," a ministry spokesman said, Reuters reported.
Citizens of the countries mentioned visit Kuwait regularly, he added.
Confusion and protests at airports greeted the executive order Trump signed last weekend to bar for 90 days entry into the United States by travelers from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
Representatives of the proscribed countries as well as several neighboring nations condemned the move, but Trump on his Twitter account said the initiative enjoyed support in the region.
"Interesting that certain Middle-Eastern countries agree with the ban. They know if certain people are allowed in it's death & destruction!" he wrote.
The United Arab Emirates was one country which did publicly give the ban a measured response. Foreign Minister Sheikh Abdullah bin Zayed called the ban an internal US matter which did not target Muslims.