Al Thani reportedly hailed Iran as an "Islamic power" and criticized US President Donald Trump's policy towards Tehran.
"The great escalation from the confusing and confused brother country and the request for political protection from two non-Arab countries and military protection from one of them could be a new tragic and comic chapter", Anwar Gargash, UAE minister of state for foreign affairs, wrote on Twitter, referring to Iran and Turkey.
The global agency Standard and Poors announced Wednesday that it lowered its rating on Qatar's long-term debt to AA-minus because of the country's dispute with its neighbours.
The incident triggered a diplomatic row between Qatar and its neighbours.
Qatar vehemently denies any such backing.
Mr Al Qassemi also warned Qatar should not rely on hosting 10,000 American troops at its al-Udeid Air Base as protection against the Arab nations lined up against it.
UN Secretary-General Antonio Guterres on Thursday joined worldwide calls to resolve tensions between Qatar and other Gulf Arab states, and said he was ready to support any diplomatic efforts "if desired by all parties".
Gargash said measures taken against Qatar this week were not aimed at seeking new leadership in Doha.
Trump is continuing to talk to all partners in the Middle East to de-escalate tensions, a White House spokeswoman said, but gave no other details.
President Trump urged Gulf unity in a call to Saudi Arabia's King Salman, US officials said on Wednesday.
The prosecutor said that the decision was made in response to Qatar's aggressive and irresponsible policies in the region.
In a sign of economic damage from the dispute, Standard & Poor's downgraded Qatar's debt on Wednesday as the country's riyal currency fell to an 11-year low amid signs that portfolio investment funds were flowing out because of the rift.
Qatar faced a similar crisis in 2014 that saw Arab countries pull their ambassadors from the country. The Maldives and one of conflict-ridden Libya's competing governments have also cut ties to Doha.
"This violation of the Security Council resolutions, if proved correct, shall definitely have a negative bearing on counter-terrorism efforts on the ground", senior Egyptian UN diplomat Ihab Moustafa Awad Moustafa told the council.
Also on Thursday, the Qatari news network Al Jazeera claimed it was under a wide-scale cyber attack that targeted "all systems".