"We are willing to sit and talk," Sheikh Mohammed bin Abdulrahman Al-Thani, the foreign minister, said Tuesday in an interview with CNN's Becky Anderson.
He said the "progressive and modern" country believes in diplomacy and promoting peace in the Middle East.
"We are not a superpower here, we are not believing in solving things with confrontation," he said.
Al-Thani insisted his country was combating terror financing and "protecting the world from potential terrorists."
But a key architect of the blockade on Qatar told CNN's John Defterios that Gulf countries are "fed up with this sort of duplicity" from Qatar.
"Very, very huge logistical, financial support for extremist groups, support also for some terrorist organizations such as al-Nusra (Front) and some organizations in Libya and in our area, such as the Sinai and other areas. This is really at the crux of the issue," the UAE's minister for foreign affairs, Anwar Gargash, said from Dubai.
"There is no more trust," he said, adding, "it is time for cooler heads, to restructure Qatar's approach on foreign policy."
Saudi Arabia, the United Arab Emirates, Egypt, Bahrain, Yemen and the Maldives said Monday that they are indefinitely severing ties with Qatar --- a Persian Gulf country of 2.4 million people, mostly foreign workers. Libya's eastern-based government, which is not internationally recognized and has no diplomatic representation in Doha, also cut ties.
Jordan announced it has decided to "lower its diplomatic representation with Qatar" and cancel the licenses of Al Jazeera's bureau in Jordan, according to a government statement. The media network is backed by the Qatar government.
Spokesman Mohammad Al-Momani said Jordan will continue to exert effort toward regional security and stability, and for Arab countries to agree on policies to end the crises in the region.
Al-Momani added, "the government hopes that this unfortunate phase will be overcome and the crisis will be resolved on solid grounds that guarantee that all Arab states cooperate to build a better future for our people."
Turkish President Recep Tayyip Erdogan criticized the decision by countries to cut diplomatic ties, according to state-run Anadolu Agency.
"I want to clearly say that we disapprove of the sanctions on Qatar," Erdogan said in Ankara. "These developments, coming at a time when we need solidarity and cooperation more than ever, are no good for any country in the region."
Gulf allies have repeatedly criticized Qatar for alleged support of the Muslim Brotherhood, a nearly 100-year-old Islamist group considered a terrorist organization by Saudi Arabia and the UAE.
Analysts say the rift is also driven by the belief that Qatar is too closely aligned with Iran.
Rejection of Saudi statement
The UAE and the other nations had another message for Qatar, Gargash said: "If we don't see that change then Qatar needs to understand that it's on its own and it has to sort of deal and run its economy and run its country on its own."
Al-Thani disputed a Saudi statement accusing Qatar of "embracing terrorist and sectarian groups aimed at de-stabilizing the region."
"With all due respect, this statement is full of contradictions, because it is saying that we are supporting Iran and on the other hand supporting the extremist groups in Syria, and (that) we are supporting the Muslim Brotherhood in Saudi or in Yemen and we are supporting the (Iranian-backed) Houthis from the other side. In all battlefields, there are adversaries," he told CNN.
"About our support to the Saudi opposition or the sectarian (movements) in al-Qatif, this is totally false information. Actually the cooperation between our security and intelligence agencies between Qatar and Saudi has been serving the purpose of the national security of Saudi."
Referring to tweets from US President Donald Trump about the diplomatic crisis
, the foreign minister said that during Trump's recent visit to the region, he and Qatar's Emir Sheikh Tamim discussed the issue "that the funding of terrorism needs to be stopped by various countries."
He said that there have been multiple reports issued by official agencies in the United States "commending our role in combating terror financing."
Kuwait's Emir, Sheikh Sabah al-Ahmed al-Jaber Al-Sabah, urged Qatar's Emir Sheikh Tamim bin Hamad Al-Thani on Monday to calm tensions with allies and refrain from escalating the diplomatic rift among Gulf Arab states, according to the Kuwait News Agency
On Tuesday, Al-Sabah was heading to Jeddah, Saudi Arabia, on a "fraternal visit" to mediate in the crisis, according to the news agency.
Scramble to get home
Qatari citizens have been told they have 14 days to leave Saudi Arabia, Bahrain and the UAE, and those countries also banned their own citizens from entering Qatar.
The last flights operated by Emirates and other major regional airlines left the capital, Doha.
Some scrambled to catch the last flights back home. Kholoud Alemadi, a Qatari-British actress, was distraught as she headed back to Doha from Dubai, where she had been starring in special shows for the Muslim holy month of Ramadan.
"I just locked my apartment and left. I just left my car," she told CNN as waited to board her flight.
Qatar is home to almost 2 million foreign nationals -- mainly workers from India, Nepal and the Philippines. A Filipino senator urged the country's government to make plans to evacuate its citizens if the standoff worsens, Philippine state media reported. The Philippines announced Tuesday that it was banning its citizens from going to work in Qatar
while it assesses the situation.
Meanwhile, Pakistan has organized special flights to bring back 550 pilgrims stranded in Qatar on their way home from Mecca.