The decision plunged Qatar into chaos and ignited the biggest diplomatic crisis in the Gulf since the 1991 war against Iraq.
Qatar wanted to solve the crisis through dialogue, the Foreign Minister added.
The Qatari government agreed to postpone a speech to its citizens in order to prioritize Kuwaiti-led mediation efforts, Qatar's foreign minister said on Tuesday.
Still, the minister struck a defiant tone, rejecting those "trying to impose their will on Qatar or intervene in its internal affairs".
With an estimated $335 billion of assets in its sovereign wealth fund and its gas exports earning billions of dollars every month, Qatar, however, has enough financial power to protect its banks.
On Monday, U.S. Ambassador to Qatar Dana Shell Smith emphasized the importance of Qatar as a U.S. ally in a series of tweets. Trump said, arguing that his visit to Saudi Arabia was "already paying off".
The Philippines said Tuesday it would not send any more workers to Qatar until the fallout from a regional political crisis became clear.
Qatari share prices closed down 7.58 percent on Monday after five Arab countries - Saudi Arabia, the UAE, Egypt, Bahrain and Yemen - announced they were cutting diplomatic ties with the gas-rich emirate.
On Monday, Saudi Arabia along with Bahrain, Egypt and the United Arab Emirates cut ties with Qatar over its alleged support for extremists.
Qatar, home to about 10,000 US troops and the host of the 2022 FIFA World Cup, criticized the move as a "violation of its sovereignty". Qatar just finished one of the stadiums that will host the tournament, though others have yet to be built.
Saudi Arabia and several other countries have cut ties with Qatar, accusing it of supporting terrorism in the Gulf region.
Qatar long has denied funding extremists, though Western officials have accused it of allowing or even encouraging funding of Sunni extremists like al-Qaida's branch in Syria, once known as the Nusra Front.
Fifa, now sponsored by Qatar Airways, declined to comment except to say: "Fifa is in regular contact with the Qatar 2022 local organising committee and the supreme committee for delivery & legacy handling matters relating to the 2022 Fifa World Cup".
The move followed severing of all land, air and sea links with Qatar and vice versa.
A number of air companies from the UAE, Egypt and Saudi Arabia said they would suspend flights to Qatar. On its website, the carrier said the suspension of its flights will take effect Tuesday.
On Tuesday afternoon, Kuwait's state news agency reported Sheikh Sabah had headed to Jeddah, Saudi Arabia, where he was to meet with Saudi King Salman in an attempt to mediate the Gulf region's diplomatic dispute.
"There is an adjustment in the Qatar Riyal after some banks have stopped buying", he said.
Pakistan has organized special flights to bring back pilgrims stranded in Qatar on their way home from Mecca, said Pakistan International Airlines chief executive officer Nayyar Hayat.
Other airlines affected by the airspace restrictions include Qatar Airways, Etihad Airways and Emirates.
Lying near the Strait of Hormuz, through which ships pass on their way to customers in Asia, the United States or Europe, Fujairah is one of the world's most important ports for the global energy market. The Al Udeid Air Base, southwest of Doha, is home to about 11,000 USA military personnel and serves as a base for US military flights to over 20 countries, including Iraq and Syria.