Foreign Minister Sheikh Mohammed bin Abdulrahman Al-Thani spoke to US Secretary of State Rex Tillerson and also met his counterpart in Germany and was due in Moscow Saturday for further talks.
On Monday, Saudi Arabia, the UAE, Egypt and Bahrain led a string of countries that cut ties with Qatar over what they say is the emirate's financing of extremist groups and its ties to Iran, Saudi Arabia's regional arch-rival.
Also named were Doha-based Muslim Brotherhood spiritual leader Yusuf al-Qaradawi and Qatari-funded charities.
The statement said the list was "an indication of the duality of Qatar policies".
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It said the list shows that Qatar "announces fighting terrorism on one hand and finances and supports and hosts different terrorist organisations on the other hand".
In all, 59 people and entities were listed.
It was released hours after Sheikh Mohammed said Doha would not "surrender" and rejected interference in its foreign policy.
"Our position on countering terrorism is stronger than many of the signatories of the joint statement -- a fact that has been conveniently ignored by the authors."
"We lead the region in attacking the roots of terrorism," the Qatari statement said.
The latest spat is unlikely to ease regional tensions in a spiralling political crisis which also threatens to involve the United States, Russia, Europe and other major players such as Turkey, a close ally of Qatar, and Iran.
Bahrain's foreign minister, Sheikh Khalid bin Ahmed Al- Khalifa, is expected in Turkey Saturday to meet President Recep Tayyip Erdogan and Foreign Minister Mevlut Cavusoglu to discuss the "latest developments in the region", Turkish officials said.
The moves taken against Doha on Monday included banning Qatar Airways from airspace and closing Qatar's only land border with Saudi Arabia, moves Doha's foreign minister termed a "blockade".
On Friday, after surprise talks in Germany with his counterpart Sigmar Gabriel, Sheikh Mohammed tweeted: "We both agree that the unjustified blockade on #Qatar is unacceptable."
And denouncing the blacklist, Sheikh Mohammed added: "There is a continuous escalation from these countries... But our strategic options are still diplomacy and dialogue."
Gabriel agreed, stressing that "this is the hour of diplomacy".
So far, European countries have largely stayed on the sidelines in the dispute.
Sheikh Mohammed is expected in Moscow Saturday to meet Foreign Minister Sergei Lavrov, and officials said Friday he also spoke with Tillerson by telephone.
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