They said Doha's refusal of their demands is proof of its links to terror groups and that they will enact new measures against it.
The Qatari government sabotaged diplomatic efforts to solve the rift, the four states said, and its refusal affirmed its continuing sabotage of the region's stability and security. The measures taken by the four states were aimed at the Qatari government but not its people, they said.
Tillerson has been in contact with the Saudi-led bloc and Qatar, where the US has its largest military base in the region, and other regional players over the last month.
He has urged the five countries to resolve their dispute, warning that it hampers operations against the Islamic State terror group.
In late June, the State Department questioned whether the boycott of Qatar was about its alleged links to terrorism or "long-simmering grievances" among the Gulf countries.
Tillerson is currently accompanying US President Donald Trump, who has sided with the Saudi-led bloc and blamed Qatar for the crisis, in Hamburg, Germany to attend the G20 summit that begins on Friday.
After the summit, the US Secretary of State will travel to Kiev and then to Istanbul before his trip to Kuwait.
- AAP