Speaking after a critical bilateral meeting with Erdogan, Merkel spoke of the need for Turkey and Germany to cooperate even further to fight against terror, including "Islamist terrorism" and Kurdistan Workers Party (PKK) militants.
"We spoke in detail about... the questions of the fight against Islamist terrorism, against every form of terrorism, also the terrorism of the PKK," she said alongside Erdogan at his palace in Ankara.
"We agree we want to cooperate, we are all affected by this. We agreed to have closer cooperation in the future," she said.
Erdogan, sitting next to Merkel, was stony-faced as she spoke.
Many Muslims oppose any equating of Islam and terror, arguing those who commit crimes purportedly in the name of Islam have nothing to do with a religion that espouses peace.
"This expression 'Islamist terror' seriously saddens us Muslims," Erdogan replied, glancing sternly at the German chancellor.
"Such an expression is not correct because Islam and terror cannot be associated. The meaning of Islam is peace."
He said it would be "saddening" if the term was used because of the crimes of the so-called Islamic State (IS) extremist group, which has been blamed for a string of attacks in Turkey over the last year.
"Please let's not use it. As long as it is used we need to stand against it. As a Muslim president personally I cannot accept that," he said.
The president's comments came after the two leaders tackled a series of hugely sensitive issues during the one day visit to Ankara by the German chancellor at a time of rising tensions between Ankara and Berlin.
His response delighted the pro-government press, with the Yeni Safak daily headlining on its website: "President Erdogan's warning to Merkel".
The phrase is controversial and previous US president Barack Obama refused to use the phrase "Islamic terrorism", saying such crimes distorted and perverted Islam.
But new President Donald Trump has not shied away from using the term, speaking of "radical Islamic terror" during the election campaign and condemning Obama for not using the term.
Indicating that her use of the phrase was no accident, Merkel used it again at her later news conference with Turkish Prime Minister Binali Yildirim, saying she had discussed the threat of "Islamist terrorism" with the premier.
But she emphasised that "no kind of suspicion against Muslims was implied" with the use of the phrase.