Qatar, which denies accusations by the UAE and some other Gulf states that it has links to militants, said in a statement to Reuters that the UAE's charge was desperate and "weak."
The UAE, Saudi Arabia and Bahrain severed diplomatic, trade and travel ties with Qatar in June, accusing it of sponsoring hardline Islamist groups, a charge Doha denies. Egypt, the Arab world's most populous state, have also joined the boycott.
Kuwaiti and U.S. attempts to ease the row have yielded little progress and media outlets backed by the opposing sides have unleashed a war of words that has aggravated tensions in the U.S-allied Gulf.
"Qatar's hosting of World Cup 2022 should include a repudiation of policies supporting extremism & terrorism. Doha should review its record," UAE Minister of State for Foreign Affairs Anwar Gargash wrote on Twitter.
"Hosting World Cup 2022 should not be tainted by support of extremist individuals & (organisations)/ terrorist figures, review of Qatar's policies a must," he added.
The World Cup is the centrepiece of a carefully crafted strategy to project Qatar onto the global stage via sport. In the run-up, Qatar is scheduled to host events across different sports aimed at improving infrastructure and expertise.
"(The) UAE's demand that Qatar give up the World Cup shows their illegal blockade is founded on petty jealousy, not real concerns," Qatar's government communications office said.
"Their weak attempts to tie the hosting of the 2022 FIFA World Cup to their illegal blockade show their desperation to justify their inhumane action," it added in a statement.
Although the countries boycotting Qatar would not have a direct way of halting the World Cup, they are major powers in regional sport and could interfere with Qatar's wider plans. Egypt is the top-ranked soccer team in Africa, and Saudi Arabia and the UAE are both in Asia's top eight.
Last month officials from the states boycotting Qatar did not turn up to the draw for a Middle East soccer tournament in Doha and said they wanted to postpone the competition that could be an early test for the World Cup hosts.
Qatar has previously said that the rift has not affected its preparations to host the tournament and that alternative sources for construction materials had been secured.
Soccer's governing body FIFA says it has been in regular contact with Qatar since the row erupted.
Gargash made his comments after a former Dubai police chief wrote on Twitter this week that the Gulf crisis could end if Doha forfeited hosting the World Cup. Gargash said the official, Dhahi Khalfan, had been misunderstood in media coverage.
(Reporting by Alexander Cornwell and Sylvia Westall; editing by Richard Balmforth)
