95 migrants from Syria, Afghanistan and Iraq had tried to reach Lesbos and Chios aboard three boats.
The remaining 42 migrants, including women and children, were picked up trying to make it to Kos.
Turkish coast guard statistics show 1,603 migrants attempted to reach the Greek islands in August, nearly twice as many as in July, AP reported.
The EU's border agency Frontex said this week the number of migrants arriving in the Greek islands has increased significantly over the last month.
Frontex said it was the "first noticeable monthly increase" since the EU-Turkey migrant deal came into effect.