The Arab country is under strict sanctions from Saudi Arabia and its allies, Egypt, the UAE and Bahrain. They accuse Qatar of backing terrorism.
Among other things, the four countries have demanded the closure of Al Jazeera TV, which is funded by the Qatari government.
Al Jazeera accused them of trying to “silence freedom of expression”.
Qatar has been under unprecedented diplomatic and economic sanctions for more than two weeks, with Iran and Turkey increasingly supplying it with food and other goods.
It denies accusations that it is funding terrorism and fostering regional instability.
The four countries also want Qatar to reduce its ties with Iran and close a Turkish military base, setting a deadline on June 23 of 10 days.
The government is reviewing the demands, a spokesman has said.
On June 21, Secretary of State Rex Tillerson had asked the four countries to make their demands “reasonable and actionable“.
However, Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman al-Thani, quoted by Al-Jazeera, said: “The US secretary of state recently called upon the blockading nations to produce a list of grievances that was <<reasonable and actionable>>.
“The British foreign secretary asked that the demands be <<measured and realistic>>. This list does not satisfy that [sic] criteria.”
Sheikh Mohammed bin Abdulrahman al-Thani said the demands were proof that the sanctions had “nothing to do with combating terrorism… [but] limiting Qatar’s sovereignty, and outsourcing our foreign policy”.
In a statement, Al Jazeera said: “We assert our right to practice our journalism professionally without bowing to pressure from any government or authority.”
Qatar’s main import routes – by land from Saudi Arabia and by sea from container ships docked in the UAE – have been disrupted and much of the surrounding airspace has been closed to its air traffic.
However, Qatar has so far avoided economic collapse by finding alternative routes.
Qatari citizens living in neighboring countries or with family living there have been hit harder, Reuters notes, because of ultimatums issued for them to leave.
Correspondents say there has been frustration in Washington over the time taken by the Saudis and others to formalize their demands.
President Donald Trump has taken a hard line towards Qatar, accusing it of being a “high-level” sponsor of terrorism.
However, the Arab states involved in the crisis are all close allies of the US while the largest American base in the Middle East is in Qatar.
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