Speaking at Chatham House in London, UAE's foreign minister also denied a Washington Post report saying that his country had been behind an alleged cyberattack on Qatar.
The UAE warned Qatar on Monday it could not belong to the Gulf Cooperation Council if it undermined regional security, calling for a "change of behaviour" but not "regime change."
Anwar Gargash, the UAE state minister for foreign affairs, also denied a Washington Post report saying that his country had been behind an alleged cyberattack on Qatar in May which sparked a crisis.
TRT World's Soraya Lennie reports from Doha.
Speaking at Chatham House international affairs think tank in London, Gargash repeated claims denied by Qatar, that the country funds extremists.
"This is our message: You cannot be part of a regional organisation dedicated to strengthening mutual security and furthering mutual interest and at the same time undermine that security," he said.
"You cannot be both our friend and a friend of Al Qaeda."
Saudi Arabia and its allies imposed sanctions on Doha on June 5, including closing its only land border, denying Qatar access to their airspace and ordering their citizens back from the emirate.
The four Arab states accuse Qatar of ties to Iran and of funding terror groups. Qatar has denied the accusations.
The Gulf crisis is the worst to hit the region since the establishment of the GCC in 1981.
"We've sent a message to Qatar. We've said we are not there to escalate. We are not after regime change. We are after a change of behaviour," Gargash said.
"We need to do that and when we do that, come back to the fold and we can work together," he added.
GCC in crisis
Gargash said there was a broader problem with financing of terror groups in the Gulf but that countries like Saudi Arabia were "dealing with it."
"The difference is that the Saudi government realises it does have an issue and the Saudi government is acting over the last years to deal with this issue," he said.
Regarding the possibility of Qatar being excluded from the GCC, Gargash said: "The GCC is in crisis, and I don't think it serves our purposes to say let's take Qatar out."
"What we really do want is we either reach an agreement and Qatar's behaviour changes, or Qatar makes it own bed and they can move on and we can move with a new relationship. But we cannot have a member who is undermining us and supporting extremism," he said.