ForwardKeys, which analyses 16 million flight reservations a day from major global reservation systems, said bookings for international arrivals to the United States over the next three months were 2.3 per cent higher than last year.
But on January 27, the day Trump issued the executive order, bookings had been 3.4 per cent ahead of the previous year, Forwardkeys data showed.
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When the travel ban was in place from January 28 to February 4, bookings to the United States dropped 6.5 per cent, including an 80 per cent slump in reservations from the seven countries listed on Trump's order and a 13.6 per cent drop from Western Europe.
On the day the curbs were lifted by a US judge, bookings from Iran surged, ForwardKeys said, leaving reservations for travel to the United States five times higher on February 3 and February 4 than the same two days a year earlier. Most of those bookings were for arrival in the United States on February 5 and February 6.
ForwardKeys CEO Olivier Jager cautioned that the data was just a snapshot of an eight-day period and it would continue to monitor the situation.
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Other groups, such as the UN World Tourism Organisation, have also warned travel demand could be hurt by US restrictions, which are still suspended pending a US appeals court hearing due to start at 2300 GMT on Tuesday.
"The ambiguity of these very latest developments introduced by President Trump is casting a shadow over the future travel demand to and from the US," said Nadejda Popova, travel project manager at Euromonitor. "The new executive order could also impact how the US is perceived as a tourism destination and how open to foreign travelers it will be in the future."
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