Tillerson sat a few feet away from Trump in the Rose Garden as the president put the blame squarely on Qatar.
Egypt on Thursday called for the United Nations Security Council to launch an investigation into accusations, denied by Qatar, that it paid a ransom of up to $1 billion to "a terrorist group active in Iraq" to release kidnapped members of its royal family.
Led by Saudi Arabia, several states in the Middle East and Africa have severed diplomatic ties with Qatar since Monday, accusing it of supporting "terrorism" and for its ties with Iran - a charge Qatar has dismissed.
A Turkish delegation would go to Qatar in the coming days to assess the situation at the base, where around 90 Turkish soldiers are now based, it said.
The UAE accused Qatar of "funding and hosting" the group in its statement announcing the severance of ties. "I decided. the time had come to call on Qatar to end its funding", he said. "They have to end that funding".
"The investigation team confirmed that the hack was carried out using innovative technological methods by exploiting an electronic gap on the website of the Qatar News Agency", the report said.
But he also said measures taken against Qatar this week by Saudi Arabia, the UAE and other Arab nations were not aimed at seeking new leadership in Doha.
More than 11,000 US and coalition forces are at al Udeid Air Base in Qatar, from which more than 100 aircraft operate. The Arab countries aren't just recalling diplomats; they're also closing airspace to Qatar and restricting access by sea. Tillerson has been tapped by Trump to help mediate the worst diplomatic crisis in the Gulf in years.
The blockade is also hindering US military action in the region and its campaign against Islamic State, he said.
Tillerson began his remarks at the State Department with a tough message for Qatar to "be responsive to the concerns of its neighbors". One U.S. intelligence official said that while Russia has the expertise and an incentive to sow division among Arab states allied with the United States, Russian hackers were available for hire to other countries and criminal groups.
The ultimatum has prompted a dramatic response by the small Persian Gulf nation, and according to a just released report by Arabic CNN (which was confirmed locally) USA officials have said they have observed increased Qatari military activity as the country placed its forces "on the highest state of alert" over fears of an imminent military incursion, according to Zero Hedge.
Shortly before Trump spoke, Secretary of State Rex Tillerson warned that the dispute was hurting the US-led war against the Islamic State terror group (banned in Russia) and urged nations to work with Kuwait as a mediator to resolve tensions.