"I want other countries to stop teaching people to kill other people", said Trump at a press conference in the White House Rose Garden with the Romanian President.
Launching an extraordinary allegation against a key US military partner, Trump derided what he called Qatar's "extremist ideology in terms of funding" terrorist groups, an accusation Qatar has repeatedly and vehemently denied.
The Islamic republic has also opened its airspace to about 100 more Qatari flights a day, after Saudi Arabia, Bahrain and the United Arab Emirates banned Qatari planes from their airspace.
The Trump administration has repeatedly said it would help the countries resolve their differences, however none of the Arab countries have expressed willingness to have the U.S.as the mediator.
Despite Tillerson's assessment that the fight against ISIS had been impacted, Pentagon officials said there has been no immediate disruption.
His comments came at the end of a week that saw Saudi Arabia, the UAE, Bahrain and Egypt sever ties with the Gulf state over concerns that it was fuelling terrorism and supporting Shia proxies of Iran.
I dunno. Trump is playing good-cop-bad-cop? In a rare public statement, Tillerson appealed to the Middle Eastern and North African governments behind the blockade of Qatar.
On Friday, Tillerson said the blockade has caused shortages of food, the separation of families and other "unintended consequences".More news: Cosby lawyers seek to paint accuser as opportunist
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"The blockade is hindering U.S. military actions in the region and the campaign against ISIS", Tillerson warned.
The mixed messages are unlikely to diffuse the diplomatic crisis and point to a broader incoherency in the region, according to Jon Alterman, director of the Middle East Program at the Center for Strategic and International Studies (CSIS).
But at the Pentagon, N avy Captain Jeff Davis said only long-term military planning was affected.
But Trump said the isolation of Qatar is not a long-term USA goal, expressing hope that the nation will "do more and do it faster" in cutting its financial ties supporting terror groups. The Qatari Embassy in Washington did not immediately respond to a request for comment.
Qatar's neighbours have also criticised it for allegedly supporting groups such as the Muslim Brotherhood and Hamas.
Qatar, which has developed an assertive foreign policy over the past decade, denies that it supports militants and says it is helping to reduce the threat of terrorism by backing groups that fight poverty and seek political reform.
Tillerson, too, faulted Qatar for allowing funds to flow to extremist groups, but in terms that were much less severe than Trump's.
The president has followed the lead of Saudi Arabia and the UAE, publically backing them in their media war with Qatar. The kingdom called the allegations "baseless".
Tillerson says the blockade is hindering US military efforts and the campaign against the Islamic State group.