"We do not want to escalate, we want to isolate," state minister for foreign affairs Anwar Gargash told journalists during a visit to Paris.
Saudi Arabia, the UAE and Bahrain broke off relations with Qatar two weeks ago and have closed land and sea borders and imposed severe restrictions on airspace.
The crisis has raised major concerns over instability in the region.
"This isolation can take years," Gargash said.
Qatar's rivals were "betting on time", but a solution could not be brokered until it abandoned its support for "extremist Islamists".
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"They support groups linked to Al-Qaeda in Syria, Libya... And in Yemen.
"This state is weaponising jihadists and Islamists, it is using this as a weapon of influence," he added.
But by applying pressure on gas-rich Qatar through sanctions, "we have a golden opportunity to break this support", he said.
Qatar strongly denies the accusations.
In the next few days, Saudi Arabia, the UAE, Bahrain and Egypt will submit a list of demands to Qatar, which is likely to include the expulsion of radical individuals.
"There must be some people who are wise in Qatar and who will prevail, hopefully within the ruling family," Gargash said.
He called for Western nations including the United States, France, Germany and Britain to help monitor any agreement reached with Qatar to ensure they are not cooperating with jihadists.
"They have the diplomatic clout and technical know-how," Gargash added.
He said that despite the row, the Gulf nations had pledged to allow the massive US base in Qatar, where 10,000 American soldiers are based, to function normally.
The Al-Udeid base, the largest US base in the region, is a key launching pad for military strikes on the Islamic State jihadist group.