Saudi Arabia and three other Arab states have given Qatar an extra two days to accept a list of demands or face further sanctions.
They accuse Qatar of destabilising the region by supporting extremism and terrorism - which it denies.
They also want Qatar to shut the Al Jazeera TV network, close a Turkish military base and scale down Iran ties.
Qatar has responded formally but no details have been released. It has said the demands break international law.
The initial deadline for Qatar to agree to the group's 13 demands expired on Sunday.
Qatari Foreign Minister Sheikh Mohammed bin Abdul Rahman al-Thani was in Kuwait on Monday to hand over a formal response in the form of a letter from the emir of Qatar to the emir of Kuwait, the main mediator in the Gulf crisis.
In a statement released shortly beforehand, lawyers for Qatar denounced the demands and called for international condemnation.
They said the tactics were "reminiscent of the extreme and punitive conduct of 'bully' states that have historically resulted in war.
"The world must unite immediately to halt the singling out of Qatar for unjustified collective punishment and humiliation and to preserve peace, security and prosperity in the region."
Qatar has been under unprecedented diplomatic and economic sanctions for weeks from Saudi Arabia and its allies, Egypt, the United Arab Emirates (UAE) and Bahrain.
The four countries, whose foreign ministers will meet on Wednesday to discuss the situation, have accused Qatar of harbouring Islamist groups that they consider terrorist organisations - including the Muslim Brotherhood - and giving them a platform on the Al Jazeera satellite channel, which is funded by the Qatari state. Doha denies the accusations.
The imposed restrictions have caused turmoil in Qatar, an oil- and gas-rich nation dependent on imports to meet the basic needs of its population of 2.7 million. As a result, Iran and Turkey have been increasingly supplying it with food and other goods.
UAE officials have told the BBC that after the new deadline expires on Tuesday, the offer for Qatar to return to the Arab fold will be off the table, the economic and political sanctions on it will become permanent and Qatar will be ostracised by its closest Arab neighbours.
The situation is the worst political crisis among Gulf countries in decades.
What are the other demands?
According to the Associated Press news agency, which obtained a copy of the list, Qatar must also:
- Sever all ties with the Muslim Brotherhood, which has been banned in several Arab states
- Refuse to naturalise citizens from the four countries and expel those currently on its territory, in what the countries describe as an effort to keep Qatar from meddling in their internal affairs
- Hand over all individuals who are wanted by the four countries for terrorism
- Stop funding any extremist entities that are designated as terrorist groups by the US
- Provide detailed information about opposition figures whom Qatar has funded, ostensibly in Saudi Arabia and the other nations
- Align itself politically, economically and otherwise with the Gulf Co-operation Council (GCC)
- Stop funding other news outlets in addition to Al Jazeera, including Arabi21 and Middle East Eye
- Pay an unspecified sum in compensation
An unnamed official from one of the four countries told Reuters news agency that Qatar was also being asked to sever links with so-called Islamic State, al-Qaeda and Lebanese Shia militant group Hezbollah.
The demands have not been officially unveiled. Their publication has increased the friction between the two sides.
How did we get here?
- 5 June: A number of Arab countries including Saudi Arabia and Egypt cut diplomatic ties with Qatar, accusing it of destabilising the region. Measures include closing airspace to Qatar Airways
- 8 June: Qatar vows it will "not surrender" the independence of its foreign policy amid US calls for Gulf unity
- 23 June: Qatar is given 10 days to comply with a 13-point list of demands, including shutting down the Al Jazeera news network, closing a Turkish military base, cutting ties with the Muslim Brotherhood, and curbing diplomatic relations with Iran
- 1 July: Qatar's foreign minister says the state has rejected the demands, but is ready to engage in dialogue under the right conditions
- 3 July: Saudi Arabia and its allies extend by 48 hours the deadline for Qatar to accept their list of demands