"Saudi Arabia, Bahrain and the United Arab Emirates are toying with the lives of thousands of Gulf residents as part of their dispute with Qatar, splitting up families and destroying people's livelihoods and education", the London-based human rights watchdog said.
Earlier this week, Saudi Arabia cut diplomatic relations with Qatar, accusing the country of supporting terrorism.
Qatar will pay the Ashcroft Law Firm $2.5 million (2 million pounds) for a 90-day period as the country seeks to confirm its efforts to fight global terrorism and comply with financial regulations including U.S. Treasury rules, according to a Foreign Agents Registration Act, or FARA, filing on Friday with the Justice Department.
Saudi Arabia said its action followed the conclusions of last month's Arab Islamic American Summit in Riyadh, where Trump delivered a speech about Islamist extremism. "I decided. the time had come to call on Qatar to end its funding", he said. "The president is focused on ending terrorism", Tillerson said.
"The blockade is hindering USA military actions in the region and the campaign against ISIS", Tillerson said, without providing details. "Families are being forcibly separated and children pulled out of school", he said.
Mr Tillerson also said the blockade by Qatar's neighbours was "hindering USA military action in the region and the campaign against Isis". But at the Pentagon, a spokesman, Navy Capt. Jeff Davis, said only long-term military planning was affected.
Kuwait's emir is working to mediate the Gulf crisis around Qatar, which is home to a major USA military base and is the host of the 2022 FIFA World Cup.
A Turkish delegation would go to Qatar in the coming days to assess the situation at the base, where about 90 Turkish soldiers are now based, it said.
There was no immediate reaction from Qatar, which hosts some 10,000 US troops.
Responding to Tillerson's comments, Erdogan said, "Tillerson's comments on Qatar is positive but not enough, all the sanctions must be halted completely".
Tillerson, who has been tapped by President Donald Trump to help mediate the crisis, also faulted Qatar for allowing funds to flow to extremist groups, echoing the complaint that Saudi Arabia, Bahrain, Egypt and the United Arab Emirates have cited in cutting off ties to Qatar.
He did urge Qatar to be "responsive to the concerns of its neighbors" and to immediately crack down on extremist funding.
Qatar does not support terrorist groups, it stressed, pointing out that "our position on countering terrorism is stronger than numerous signatories of the joint statement-a fact that has been conveniently ignored by the authors". It's the worst diplomatic crisis to hit Gulf Arab states in decades.
In Moscow, Russia's Foreign Minister Sergey Lavrov said his country will undertake every effort to help ease the tensions. Meanwhile, a statement from European Union foreign policy chief Federica Mogherini said the bloc was calling on all sides to "avoid any further escalation and engage in a political dialogue".