"This list is connected to Qatar and serves suspicious agendas in an indication of the duality of Qatar policies", said the statement early Friday from Saudi Arabia, the United Arab Emirates, Egypt and Bahrain.
White House spokesman Sean Spicer told a regular press briefing on Tuesday that the USA wants to see the diplomatic row between Qatar and the other Gulf nations "deescalated and resolved immediately". Other U.S. officials have said Qatar has already taken some steps to reduce terror funding but that the steps are insufficient.
Trump added that "all reference was pointing to Qatar". Families are being forcibly separated, and children pulled out of school.
Tillerson's earlier statement that the "blockade" of Qatar is hurting USA economic and military efforts in the region contradicts Pentagon officials' insistence earlier in the week that there has been no impact on US operations in Qatar, or the fight against ISIS.
"We have to stop the funding of terrorism. the time had come to call on Qatar to end its funding they have to end that funding and its extremist ideology in terms of funding", said the US President.
According to the White House, Mr. Trump also reiterated the importance of the Gulf Cooperation Council (GCC), in the wake of several key GCC members, including Saudi Arabia and Bahrain, cutting off diplomatic relations with Qatar.
Tillerson said Qatar has a history of supporting groups across a wide political spectrum, including those that engage in violence, and that the emir of Qatar had made progress in halting financial support for terrorism but that he must do more.
He added: "We are not ready to surrender, and will never be ready to surrender, the independence of our foreign policy".
Qatar on Friday dismissed as "baseless" a terrorism blacklist published by Saudi Arabia and its allies which linked individuals and organisations in Doha to support for Islamist militant groups.
The Trump administration is insisting that Qatar drop all connections with the Muslim Brotherhood - both inside its borders and in other countries, including Jordan, CBS News foreign affairs correspondent Margaret Brennan reports.
Trump's tweets seem to have been issued in haste without consideration for USA ties to Qatar which is home to an important United States air base. Sisi has been angered by Qatar's support for the Muslim Brotherhood, which Egypt says is a terrorist organisation.
It wasn't immediately clear how Trump's sharp condemnation might affect US cooperation with Qatar, which hosts some 10,000 USA troops and a major US air base that serves as a staging ground for operations in Syria, Iraq and Afghanistan. Saudi Arabia said its action followed the conclusions of last month's Arab Islamic American Summit in Riyadh, where Trump delivered a speech about Islamic extremism. The nations withdrew their ambassadors from Qatar and cut off air, sea and land travel to the peninsular nation, which is rich in oil but depends heavily on imported food.
"They will not have a positive impact on the region but a negative one", the minister said while on a visit to Germany.