Tsipras, who arrived in Turkey late Tuesday, held a 40-minute meeting with the Istanbul-based Ecumenical Patriarch Bartholomew I, the spiritual leader of the world`s Orthodox Christians.
He then headed to Ankara to hold talks with his Turkish counterpart Ahmet Davutoglu and President Recep Tayyip Erdogan.
In Ankara, Tsipras will urge Turkish leaders to impose stricter controls on human smuggling into Europe after the Paris attacks threw a security spotlight on the migrant flow.
"We need to talk more about how to fight trafficking networks and how to coordinate and cooperate on the level of migration, police and coastguard authorities," Tsipras wrote in pro-government Daily Sabah.
Turkey is the main launching point for migrants coming to Europe, and currently hosts over two million Syrian refugees.
In return for its help, Turkey has demanded the EU provide three billion euros ($3.3 billion) a year in funding, visa-free travel for Turkish nationals and an end to the stalemate in talks for Ankara to join the 28-nation bloc.
More than 650,000 migrants and refugees, have reached the Greek islands so far in 2015 using the eastern Mediterranean route, the International Organisation for Migration (IOM) said earlier this month. Of those, 512 people died.
Just a few hours after Tsipras arrived in Turkey, at least nine people, including four children, drowned when a boat carrying migrants from Turkey sank off the Greek island of Kos.
Athens fears coming under new EU pressure over the migrant crisis after the discovery at the scene of one of Friday`s Paris attacks of a Syrian passport registered in the Greek island of Leros on October 3.
Tsipras and Davutoglu attended an international football friendly between Turkey and Greece on Tuesday, but the match was overshadowed by some Turkish fans booing the Greek team during a minute of silence for the victims of the Paris attacks.
Greece and Turkey have a fraught history going back centuries, with disputes over maritime borders and the partition of Cyprus. But tensions between the NATO allies have eased considerably in recent years.
Greek PM in Turkey to discuss migrant crisis
18 November 2015
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Greek Prime Minister Alexis Tsipras held talks Wednesday with the Greek orthodox patriarch as he embarked on his first official visit to Turkey set to be devoted to grappling with the huge flow of refugees entering his country from Turkish territory.
