"We don't see a military solution as an option" to the crisis, Sheikh Mohammed said.
Bahrain, Egypt, Saudi Arabia and the United Arab Emirates said they sanctioned the groups and individuals because of "the continuous and ongoing violations of the authorities in Doha of Qatar's commitments and obligations".
Qatar hasn't commented on this report and Russian Federation denies involvement.
The network also said Thursday night that its websites had come under a sustained cyberattack.
The Gulf crisis has sparked fears of military escalation in an already volatile region.
Kuwait - which unlike most of its fellow Gulf Cooperation Council members has not cut off ties with Qatar - has been leading efforts to mediate. On Wednesday, Emirati officials shut down the airline's offices in the UAE.
US President Donald Trump, who had initially backed the measures against Qatar in a tweet, called Sheik Tamim on Wednesday with an offer "to help the parties resolve their differences".More news: Do not disturb while driving feature for iPhone welcomed by Brake
Pakistan today rejected as "fabricated and baseless" reports that it plans to deploy its troops in Qatar amid diplomatic tensions in the Middle East.
Turkey, which works closely with Qatar in the energy sector, has walked a fine line between defending Qatar and abstaining from openly antagonising Saudi Arabia. "They are hosted here. for peace talks". Doha is the world's largest exporter of natural liquefied gas.
Analysts say the crisis is an extension of a pre-existing dispute which saw Saudi Arabia, the UAE and Bahrain temporarily recall their ambassadors from Doha in 2014 over Qatari support for Egypt's Muslim Brotherhood. "This is the biggest testimony to US failure in the Gulf", the diplomat told Reuters on condition of anonymity.
Qatar dismissed the terror listing as part of "baseless allegations that hold no foundation in fact", standing by earlier defiant statements by its top diplomat to The Associated Press that Arab nations had no "right to blockade my country".
"This is not about regime change - this is about change of policy, change of approach", state minister for foreign affairs Anwar Gargash said.
The diplomatic crisis, the worst since the 1990 invasion of Kuwait by Iraq and the subsequent Gulf War, has seen Arab nations and others cut ties to Qatar, which hosts a major US military base and will be the host of the 2022 FIFA World Cup.
"We do not consider sanctions against Qatar effective".