Anwar Gargash, the United Arab Emirates state minister for foreign affairs, issued the warning more than two weeks into the oil-rich region's worst diplomatic crisis in years.
He also accused Qatar of leaking a document containing the demands by Saudi Arabia, the UAE, Bahrain and Egypt, which have cut diplomatic ties with the gas-rich state accusing it of sponsoring terrorism.
Qatar strongly denies such charges.
The demands have not been officially unveiled but Doha- based Al-Jazeera news channel said overnight Thursday they were handed to Qatar by Kuwait, which is mediating in the crisis.
"The leak (of the demands by Qatar) is an attempt to abort the mediation in a childish act that we have grown accustomed to from our brother," Gargash wrote on Twitter.
"It would be wiser that (Qatar) deal seriously with the demands and concerns of the neighbours or a divorce will take place," he said.
On June 5, Saudi Arabia and the UAE led a severing of all links with Qatar for allegedly supporting groups, including some backed by Iran, "that aim to destabilise the region".
Saudi Arabia regularly accuses Iran, its regional rival, of interference throughout the Middle East.
As well as cutting diplomatic ties, Qatar's neighbours closed their air space to Qatari carriers and blocked the small but gas-rich emirates' only land border, vital for its food imports.
"The brother (Qatar) must realise that the solution for its crisis lies not in Tehran or Beirut or Ankara or Western capitals or in media outlets, but in regaining the trust of its neighbours," Gargash said.
"It is not possible to accept that the brother continues as the Trojan horse" in the Gulf or as a funder and "platform for an extremist agenda", he added.
Ankara and Washington have also been trying to help broker a solution to the crisis within the Gulf Cooperation Council which groups Qatar with Bahrain, Kuwait, Oman, Saudi Arabia and the UAE.
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