The statement was likely to fan concerns over Turkey's large-scale crackdown on followers of the cleric, Fethullah Gulen, and raise questions over whether the government would start a witch-hunt based on an army of informants.
"You may have friends from the community," Erdogan told a group of Turkish exporters. "I say you have to expose them. You have to inform them to prosecutors and the police. Why? This is our patriotic duty."
"We have no right to show pity toward those who showed no mercy to their country or people."
The government launched a sweeping crackdown after the coup, targeting followers of Gulen, whom it accuses of orchestrating the attempted putsch that left more than 270 dead.
Also Read
Some 16,000 people have been formally arrested in connection to the coup, while thousands more have been detained for questioning.
Tens of thousands of people with suspected links to Gulen have also been suspended or dismissed from their jobs in the judiciary, media, education, health care, military and local government.
Gulen, who runs a network of charities and schools worldwide, has repeatedly denied involvement in the coup.
The scope of the crackdown on the movement has raised alarm in European countries and among human rights groups, which have urged restraint.
Erdogan has lashed out at the criticism and has complained of a lack of solidarity and support from allies for the elected government.
Speaking to the exporters, Erdogan urged the businessmen to inform "prosecutors and police" on Gulen supporters they know, and to inform business contacts abroad that the Gulen movement was "not only a threat to our country but to the whole world.