Turkey's president said his country "admires and embraces" Qatar's attitude, while slamming the demands by arguing they contradict global law.
Erdogan said Turkey had offered to set up a military base in Saudi Arabia as well as Qatar, but Riyadh had not responded.
"We approve and appreciate the attitude of Qatar against the list of 13 demands", Erdogan said. "If Saudi Arabia wants us to have base there, a step toward this also can be taken", he told reporters.
Speaking after Eid al-Fitr prayers in Istanbul, President Recep Tayyip Erdogan called the demand to pull the Turkish troops "disrespectful" and said his country would not seek permission from others when making its defense cooperation agreements.
Qatar faces the prospect of diplomatic isolation in the long-term if it does not accept the demands made by its Gulf neighbours to end an ongoing dispute, a United Arab Emirates minister warned on Saturday.More news: Michael Carrick to decide on Man Utd retirement next season
Kuwait handed the list of collective demands to Doha on Thursday, according to the official Qatari news agency QNA. Qatar itself has made it clear that it will not yield to its neighbours' demands to change policies at home or overseas.
Erdogan also said, in the address, the requests for the Turkish military base in Qatar to be closed were disrespectful.
Saudi Arabia, Bahrain, Egypt, and the UAE severed ties with Qatar on June 5, officially accusing Doha of supporting "terrorism" and destabilizing the region.
A Turkish foreign ministry statement Sunday reiterated that the deployment of Turkish troops in Qatar contributed to regional security and was not aimed at a specific country.
"Helping Qatar economically and developing ties, particularly in the private sectors of both countries, could be a common goal", Rouhani said on Sunday. "I had a little condition about my blood pressure, related to my diabetes", he said.