Turkey pulled a small military convoy out of a training base in northern Iraq that has become a new flash point as regional powers exert their influence, but refused to buckle to increasing pressure from Baghdad and Moscow to remove all its troops.

About 10 Turkish military vehicles left the camp early Monday, Turkish and Iraqi officials said, and they are moving to another base in northern Iraq. While Turkish Prime Minister Ahmet Davutoglu said the move was meant to address Baghdad’s concerns, he added that Ankara had no...