Saudi Arabia, Bahrain, Egypt and the United Arab Emirates cut off ties with Qatar, accusing it of interfering in their affairs and supporting terrorism.
Foreign diplomats have visited the region, urging a dialogue to resolve the crisis that is now in its second month. However, the al-Attiyah said "lifting the siege should precede any dialogue".
"If the blockading countries remain reluctant to lift the siege, Qatar will be compelled to resort to the available international legal procedures to lift it," al-Attiyah said in an interview with Russia Today, excerpts of which was published by Qatar's official news agency on Tuesday.
The Qatari minister ruled out the relocation of the Al-Udeid US military base from his country, Al Jazeera reported.
"The US-Qatari relations are strong," he said, going on to deny that the "acceleration of the deployment of Turkish troops in Qatar was in anticipation of any military escalation against Doha".
"The Turkish and US military presence in Qatar doesn't pose any kind of sensitivity at all," he said, aruging that the Saudi-led group has relied in its escalation on US President Donald Trump's tweets.
"They forgot that the US is a country of institutions, most of which is the department of state, which has explicitly supported the Qatari’s position," he said.
On Tuesday, Turkish President Tayyip Erdogan described his trip to the Persian Gulf "productive and successful", following two days of talks that appeared to yield no immediate progress towards healing the rift.
"The visits on the Persian Gulf tour were productive and successful," Erdogan told lawmakers from his ruling AK Party at a parliamentary meeting.
"The contacts we have made during this visit have been useful, and we will continue our efforts for the stability and peace of the region with increasing determination."
Turkey has been Qatar's most powerful ally in the dispute.