"No-one has any interest in prolonging this crisis any more," said Erdogan before leaving Istanbul airport on the two-day trip that will take him to Saudi Arabia, Kuwait and then Qatar.
He accused "enemies" of seeking to "fire up tensions between brothers" in the region.
On June 5, Saudi Arabia, Bahrain, the United Arab Emirates and Egypt cut ties with Qatar accusing it of backing terrorism and fostering ties with their Shiite rival Iran. Doha denies the claim and has been strongly backed by Ankara throughout the standoff.
The crisis with Qatar has put Turkey in a delicate position and Erdogan has repeatedly said he wants to see the end of the dispute as soon as possible.
Over the last years, Qatar has emerged as Turkey's number one ally in the Middle East, with Ankara and Doha closely coordinating their positions on a number of issues including the Syria conflict where both are staunch foes of President Bashar al-Assad.
Crucially, Turkey is in the throes of setting up a military base in Qatar, its only such outpost in the region. It has sped up the process since the crisis began and reportedly now has 150 troops at the base.
But Turkey, which is also going through a turbulent time with the European Union and the United States, also does not want to wreck its own relations with regional kingpin Saudi Arabia.
"As the elder statesman in the Gulf region, Saudi Arabia has a big role to play in solving the crisis," said Erdogan, with explicitly criticising the kingdom.
Erdogan said he supported the mediation efforts of Kuwait's Emir Sheikh Sabah Al-Ahmad Al-Sabah, a possible indication Ankara sees Kuwait as the key to solving the crisis.
Qatar's Emir Sheikh Tamim bin Hamad Al-Thani said Friday he was ready for talks to resolve the crisis so long as the emirate's sovereignty is respected.