Italian priest Andrea Santoro, 59, was shot twice in the entrance of the Santa Maria Catholic Church in the northern city of Trabzon and the Vatican's ambassador to Turkey said the gunman shouted "God is great" as he fired his pistol.
"We don't have much to go on to make a proper interpretation of what happened. However, the only element which a collaborator of Father Santoro's mentioned to me is that the person who killed him shouted 'Allahu Akhbar'," Monsignor Antonio Lucibello was quoted as saying by Italy's ANSA news agency.
The acclamation, used in prayer, is also employed as a rallying cry by Islamic militants.
"There are claims that the incident may be related to the cartoons," Trabzon Governor Huseyin Yavuzdemir told Anatolia news agency. "This will become clear when the suspect is captured."
The Turkish government "ferociously" condemned the murder and promised to find the perpetrator, described by witnesses as a male in his late teens who ran away after the shooting.
A person who was inside the 19th century church told the police the assailant fired three shots as the priest opened the gate before evening prayers, Anatolia reported.
Two bullets hit the victim and a preliminary examination established that he died of a wound in his chest, it said.
The Vatican embassy in Ankara said Santoro was originally from Piverno, a small town near Rome.
Mr Yavuzdemir said the police had information the priest had been threatened by locals in the past over alleged efforts to convert Muslims, but there was no indication the church was involved in missionary work.
"The security forces are investigating the people who have threatened and criticised him," he said, adding that Father Santoro had not asked for protection from the police.
Police stepped up security measures at main crossroads in Trabzon and at the entrances and exits of the city, Anatolia reported.
"We ferociously condemn this murder committed in a religious sanctuary and against a man of religion," Justice Minister Cemil Cicek, who is the government's spokesman, told Anatolia.
"The government is making all possible efforts to shed light on this incident and find out who perpetrated it and why," he said.
Attacks condemned
Earlier on Sunday Prime Minister Recep Tayyip Erdogan condemned the torching of Danish and Norwegian missions in Syria and Lebanon and warned that violence over the Prophet Mohammed cartoons would further undermine efforts to bring different cultures closer.
Mr Erdogan maintained his criticism of the drawings but stressed that "torching and destruction cannot be a means of correcting mistakes", Anatolia reported.
"The solution should be at the negotiating table, in diplomacy," he said.
Turkey, a strictly secular state with a predominantly Muslim population, sees itself as a bridge between East and West and is seeking to join the European Union.
Foreign Minister Abdullah Gul convened an emergency meeting with senior diplomats late Sunday to discuss what initiatives Turkey can undertake to help bring an end to the cartoon crisis, officials said.
In a statement condemning the priest's murder, the foreign ministry insisted that Turkey remained an example of peaceful co-habitation between Islam and other religions.