The meeting of foreign ministers in Cairo comes on the day a deadline expires for Qatar to accept a list of demands or face further sanctions, reports BBC
The demands to Qatar include shutting down the news media outlet Al Jazeera and scaling down ties with Iran.
Qatar has called the list of demands "unrealistic and not actionable".
Qatar is accused of destabilising the region by supporting extremism and terrorism - which it denies.
The tiny gulf emirate has been under unprecedented diplomatic and economic sanctions from Saudi Arabia, Egypt, the UAE and Bahrain.
The restrictions have caused turmoil in the Gulf state, which is dependent on imports to meet the basic needs of its population of 2.7 million.
On Monday, Saudi Arabia and its Arab allies gave Qatar an extra two days to accept their ultimatum for restoring relations, after an earlier 10-day deadline expired.
The authorities in Doha have responded to the demands - but no details have been publicly released. Qatar has said the demands break international law.
On Tuesday, Qatari Foreign Minister Sheikh Mohammed bin Abdul Rahman al-Thani described the demands as unrealistic.
"It's not about terrorism, it's talking about shutting down the freedom of speech," he said.
The four countries accuse Doha 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.
Qatar denies the accusations.
As a result of the sanctions, Iran and Turkey have been increasingly supplying Qatar with food and other goods.
On Tuesday, Qatar announced plans for a steep rise in Liquefied Natural Gas (LNG) production capacity over the coming years.
The country is the world's leading producer of LNG.


