Qataris crowded into supermarkets to stock up on goods, fearing shortages.
Despite Trump's comments, the White House later called on the countries involved to reduce tensions and resolve the crisis "immediately", while the State Department said that the relationship with Qatar was "solid" and that Washington "continues to cooperate" with that country. But in an attempt to avoid alienating other Persian Gulf states by coming down hard on them, he offered to step in as a peacemaker.
Trump spoke by telephone with Saudi Arabia's ruler King Salman later Tuesday in an exchange of notably different tone from the USA president's earlier remarks on Twitter.
Qatar Airways, one of the region's major long-haul carriers, has suspended all flights to Saudi Arabia, the United Arab Emirates, Egypt and Bahrain until further notice.
A Qatari official said the rift was pushing Doha in the direction of leaving the six-state Gulf Cooperation Council, "with deep regret".
The airline can operate flights linking Indonesia to destinations apart from the countries that have "a diplomatic problem with Qatar", it added in an emailed statement.
For decades Saudi Arabian politics in Middle East has been a reductive "us or them" ultimatum delivered to nations over their relations with Iran.
Qatar is also a major regional diplomatic player and global investor and is set to host the World Cup, football's biggest tournament, in 2022.
Saudi Arabia, the powerhouse among those cutting ties to Qatar, said it did so due to the country's "embrace of various terrorist and sectarian groups aimed at destabilizing the region", including the Muslim Brotherhood, al Qaeda, Daesh and militants supported by Iran in the kingdom's restive Eastern Province. The immediate break of the diplomatic ties with Iran was also reportedly one of the conditions laid down by Riyadh.
"The measures are unjustified and are based on false and baseless claims", Qatar said in response to Monday's announcement. "The most appropriate way for the Gulf Cooperation Council countries to solve their internal issues is through dialogue".
"On this scale, it's unprecedented", said Hatoon al-Fassi, a Saudi historian of Gulf Affairs and Women's Studies at Qatar University.
Fellow Gulf states are also reported to have been angered by a huge ransom paid by Doha earlier this year to secure the release of a hunting party, which included members of the Qatari royal family, kidnapped in southern Iraq.
The ransom, which Iraqi officials said was in the "hundreds of millions of dollars", was believed to have been paid to militias with close ties to Tehran.