"No one has the right to intervene in our foreign policy," Sheikh Mohammed bin Abdulrahman Al-Thani told AFP.
"We don't see a military solution as an option" to the crisis, he added.
A top United Arab Emirates official on Wednesday told AFP that the unprecedented measures against Qatar aim to pressure Doha into making drastic policy changes.
"This is not about regime change -- this is about change of policy, change of approach," state minister for foreign affairs Anwar Gargash said, accusing the government in Doha of being in "denial".
More From This Section
Qatar denies having any ties to extremists.
The UAE's Gargash today told AFP the measures against Doha were limited to diplomatic and economic ties, but warned that no one could project the "dynamic of a crisis".
"Like any crisis, you cannot really control the dynamic... This is one of the dangers of any crisis. There is no intention for us to seek anything but what we look at as economic spheres of activities," he said.
Saudi Arabia has also closed off Qatar's only land border, a crucial lifeline for food imports.
Sheikh Mohammed said Qatar could nonetheless survive "forever", adding that it respected international agreements and would continue supplying liquefied natural gas to the UAE.
Qatar is the world's largest exporter of natural liquefied gas.
The emirate is also home to leaders of Egypt's Muslim Brotherhood, the Palestinian Hamas and the Afghan Taliban.
Analysts say the crisis is in part 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 the Muslim Brotherhood.