The manoeuvres are aimed at preparing Qatar's armed forces to defend "vital economic, strategic and infrastructure facilities," state-owned newspaper Al-Sharq reported.
Turkey's parliament fast-tracked legislation on June 7 to allow hundreds of troops to be deployed to a military base in Qatar, set up as part of an agreement signed in 2014, in a show of support for Qatar, which is also home to the biggest US air base in the region, Reuters reported.
Ankara has said it will deploy 3,000 ground troops at the base to serve as a venue for joint training exercises and to support anti-terrorism efforts.
Turkey stood by Qatar after Saudi Arabia, Egypt, the United Arab Emirates and Bahrain called it a supporter of terrorism, which Doha denies, and cut off diplomatic ties and transport links.
The countries want Qatar to close down the Turkish base, curb relations with Iran and close the Al Jazeera TV channel.
But Turkey and Qatar maintain ideological ties, as Turkey's ruling party has Islamist roots and Doha is a main backer of the Muslim Brotherhood, which its Arab opponents deem a terrorist organization.