The council includes Qatar, Saudi Arabia, the United Arab Emirates, Bahrain, Oman and Kuwait.
In the wake of Trump's first trip overseas after taking office, Egypt, Saudi Arabia, the United Arab Emirates and Bahrain accused Qatar of supporting terrorism and broke off diplomatic relations. The Saudis joined Egypt, Bahrain, Yemen and the UAE in cutting ties to the country.
Trump said he'd told the kings, presidents and prime ministers that funding "Radical Ideology" can't be tolerated, and "Leaders pointed to Qatar - look!"
On Monday, risk consultancy the Eurasia Group said, "The recent measures by the anti-Qatar alliance signal commitment to forcing a complete change in Qatari policy or creating an environment for leadership change in Doha". "Perhaps this will be the beginning of the end to the horror of terrorism!"
But even with the White House's attempts at clarification, Trump's statements raise questions as to how the move impacts the US military base in Qatar, as well as how the diplomatic stress serves American priorities and goals in the region.
The Gulf countries have ordered their citizens out of Qatar and gave Qataris overseas 14 days to return home.
The Qatari government has no immediate response to Trump's tweet.
On Monday, Saudi Arabia, Bahrain, and the UAE gave Qatari nationals two weeks to leave, banned their own citizens from travelling to Qatar, and cut all transport links.
Qatar's stock market rebounded in early trade on Tuesday after plunging the previous day but the Qatari riyal fell against the USA dollar.
Qatar may seem like a bit player in the world of Middle Eastern politics, but there's good reason Washington would not want Trump to alienate the gulf nation.
The regional spat has complicated consequences for the West, and especially the United States.
Qatar is home to the biggest United States airbase in the Middle East, Al-Udeid, where some 10,000 military personnel are stationed.
Last month, the website of Qatar's official news agency was allegedly hacked by unknown individuals who reportedly published statements falsely attributed to its emir, Sheikh Tamim Bin Hamad al-Thani.
Navy Capt. Jeff Davis, a Pentagon spokesman, expressed gratitude to Qatar for supporting the USA presence, outlining no plans to adjust American military posture. Qatar even extradited a political dissident to Saudi Arabia on the same day it was accused of being pro-Iranian.
Analysts have said Qatar Airways will lose millions of dollars in revenue from flight cancellations caused by the scrapping of its license by Saudi Arabia.
The UAE General Civil Aviation Authority (GCAA) is yet to revoke licences given to Qatar Airways similar to the step taken by its Saudi counterpart. Al-Thani's other bunk quotes concerned Donald Trump, questioning whether #45 could survive an entire presidential term and claiming that the Donald had "no wisdom" when it comes to dealing with Iran.