With backing from Turkey and Iran, Qatar has described the pressure by its larger neighbours as an "illegal blockade" aimed at curbing its sovereignty.
Iranian President Hassan Rouhani voiced support on Sunday for Qatar in its confrontation with Iran's rival Saudi Arabia and its allies, saying a "siege of Qatar is unacceptable."
Saudi Arabia, the United Arab Emirates, Egypt and Bahrain cut ties with Qatar on June 5, accusing it of supporting terrorism based on its ties with the Muslim Brotherhood, Hamas and the Taliban, allegations Qatar denies.
They have since issued 13 demands including closing Al Jazeera television, curbing relations with Iran, shutting a Turkish army base and paying reparations.
Qatar has described the pressure by its larger neighbours as an "illegal blockade" aimed at curbing its sovereignty, and said that the ultimatum by its Gulf neighbours was "unreasonable."
"Tehran stands with the Qatari nation and government ... We believe that if there is a conflict between regional countries, pressure, threats or sanctions are not the right way to resolve differences," Rouhani told Qatar's leader, Tamim bin Hamad al-Thani, in a telephone call.
"The siege of Qatar is unacceptable to us ... The airspace, land and sea of our country will always be open to Qatar as a brotherly and neighbouring country," Rouhani said.
TRT World's Andrew Hopkins reports on the latest developments from Qatar's capital, Doha.
Doha, whose neighbours have closed their airspace to Qatari flights, has said it was reviewing the list of 13 demands, but said it was not reasonable or actionable.
Predominantly-Shia Iran and predominantly-Sunni Saudi Arabia accuse each other of subverting regional security and support opposite sides in conflicts in Syria, Yemen and Iraq.
Turkey backs Qatar
Turkish President Recep Tayyip Ergodan on Sunday also backed Qatar's response and said calls to shut down a Turkish military base there were disrespectful.
"We consider these demands are against international law," Erdogan told reporters after Eid al-Fitr prayers in Istanbul.
"It is a breach of Qatar's sovereign rights."
Erdogan said Turkey had offered to set up a military base in Saudi Arabia as well as Qatar, but Riyadh had not responded.
"Even though they still didn't come back to us on this, asking Turkey to pull back its troops (from Qatar) is disrespectful against Turkey," he said.
US tones down its rhetoric
US Secretary of State Rex Tillerson on Sunday called on Qatar and a Saudi-led group of four Arab states to sit down together in order to try to reach a resolution.
"A productive next step would be for each of the countries to sit together and continue this conversation," Tillerson said in a statement.
"We believe our allies and partners are stronger when they are working together towards one goal which we all agree is stopping terrorism and countering extremism."