Neighbours including Saudi Arabia and the United Arab Emirates (UAE) have closed their airspace to Qatari planes.
Meanwhile, US President Donald Trump has said he was told during his recent visit to Saudi Arabia that Qatar was funding “radical ideology”.
“During my recent trip to the Middle East I stated that there can no longer be funding of Radical Ideology. Leaders pointed to Qatar – look!” he tweeted.
Kuwait – one of the Gulf countries not involved in the dispute – has offered to mediate talks, and Qatar said it was receptive to dialogue.
In an interview with Qatar’s al-Jazeera network, the Qatari foreign minister said Kuwait’s emir would travel to Saudi Arabia on Tuesday for talks.
Sheikh Mohammed Bin Abdulrahman al-Thani told Al Jazeera that Qatar was seeking “a dialogue of openness and honesty”.
Six countries – Bahrain, Saudi Arabia, the UAE, Yemen, Libya’s eastern-based government and the Maldives – cut diplomatic ties with Qatar on Monday.
Bahrain, Saudi Arabia and the UAE have given Qatari nationals two weeks to leave, and banned their own citizens from travelling to Qatar.