Qatar's backing of Islamists dates to a decision by the current ruling emir's father to end a tradition of automatic deference to Saudi Arabia, the dominant Gulf Arab power, and forge the widest possible array of allies.
Soccer's governing body Federation Internationale de Football Association said it remained in regular contact with Qatar, which will host the 2022 World Cup.
Analysts say President Donald Trump's recent visit to Saudi Arabia emboldened hawkish Saudi royals by positioning America squarely with Sunni Arab countries against Iran.
Since 2003 Udaid airbase in Qatar has been a forward headquarters of US Central Command and hosts about 10,000 American troops. Its al-Udeid Air Base serves as a launching pad for coalition jets bombing IS sites in Iraq and Syria.
Along with Egypt, however, the UAE and Saudi Arabia could be vulnerable to retaliation, being highly dependent on Qatar for liquefied natural gas.
Qatar are now bottom of their qualifying group, with only South Korea, Syria and China to play.
Iran also urged Qatar and its neighbours to talk. The chief worry among them is the Muslim Brotherhood, a Sunni Islamist political group opposed to monarchical rule.
Saudi Arabia, Egypt, the United Arab Emirates and Bahrain severed their ties with Qatar Monday, accusing it of supporting terrorism, in an unprecedented breach between the most powerful members of the Gulf Cooperation Council.
Some Gulf news coverage seemed to support regime change in Qatar, and accused its emir of holding a secret meeting with Iranian Revolutionary Guard commander Gen. Qassem Soleimani.
They claim Qatar is funding militant groups which operate in their countries, such as Al-Qaeda, the Muslim Brotherhood and the so-called Islamic State, which Qatar denies.
Gas-rich Doha, which has long exercised an independent streak in its foreign policy, last month denied comments which appeared on its official news agency questioning United States hostility towards Iran.
There could be long-term economic consequences for Qatar, which would affect the millions of migrant workers and expatriates living there.
Saudi Arabia closed its land border with Qatar, through which the tiny Gulf nation imports most of its food, sparking a run on supermarkets. A change in leadership could raise questions about the future of the USA base and potentially deprive Hamas of its main benefactor.
Saudi Arabia, the United Arab Emirates and Bahrain said they were cutting air, sea and land transport links with Qatar, while Egypt said it was closing its air space and sea ports to all Qatari transport.
Qatar Airways, one of the region's major long-haul carriers that routinely flies through Saudi airspace, did not immediately respond to a request for comment.
UAE carriers Emirates, Etihad, flydubai and Air Arabia, as well as Saudi Airlines, have said they will halt flights to and from Doha starting from Tuesday morning.
Further, Qatar's willingness to welcome organizations such as Hamas, which Washington brands a terrorist group, and the Taliban, which has fought USA forces in Afghanistan for more than 15 years, allows contacts with such groups when needed. The White House said on Monday it was committed to working to de-escalate tensions in the Gulf. Qatari media published a cartoon mocking Saudi King Salman for spreading "fake news". The details of the agreement that ended that standoff were never made public, but it included promises that Qatar would end its support for the Brotherhood.