It also demanded the launch of a public inquiry into foreign funding of extremism, putting pressure on the government which has so far refused to publish its own report into foreign funding of terrorism.
In a statement attributed to an unnamed senior foreign ministry official released later Friday, Qatar called allegations made by the quartet against it false and tantamount to "defamation in contradiction with the established foundations of worldwide relations".
"We have sovereign wealth funds of 250 percent of gross domestic product, we have Qatar Central Bank reserves, and we have a ministry of finance strategic reserve", the country's finance minister Ali Sharif al-Emadi told The Times, after his country rejected the list of demands.
British Foreign Secretary Boris Johnson is in Saudi Arabia for the first in a series of meetings with Gulf leaders over the region's political crisis.
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Kuwaiti Acting Premier and Foreign Minister Shaikh Sabah Khaled Al-Hamad Al-Sabah expressed the stance during a phone call with Egyptian Foreign Minister Sameh Shoukry, the Egyptian news agency (MENA) reported.
His Highness the Emir Sheikh Tamim bin Hamad al-Thani and the UK Foreign Minister Boris Johnson discussed on Saturday the latest developments of the GCC crisis and its implications in terms of regional and global stability.
Al-Marri said that the decision to pursue compensation for damages was not tied to current state of negotiations between Qatar and the blockading countries. Qatar has denied the allegations, and says the bloc's ultimatums are an affront to its sovereignty. They did not specify what those steps could include, though officials have previously suggested they could intensify efforts to isolate Qatar economically.
Earlier, four Arab nations, including Saudi Arabia, have said that they would continue their diplomatic and economic blockade of Qatar after the nation gave a "negative" response to their list of demands.
The four countries pulled their diplomats from Qatar, suspended all flights to and from Doha and ordered all Qataris to repatriate within 14 days.