The Cumhuriyet newspaper published footage on its website on Friday which it said showed gendarmerie and police officers opening crates of what it described as weapons and ammunition on the back of three trucks belonging to MIT.
"The individual who has reported this as an exclusive story will pay a high price for this," Erdogan said in a television interview with state broadcaster TRT late on Sunday.
"I will not let this go."
Witnesses and prosecutors have alleged that MIT helped deliver arms to parts of Syria under rebel control during late 2013 and early 2014, quoting a prosecutor and court testimony from gendarmerie officers.
Cumhuriyet said the video was from Jan. 19, 2014 but did not say how it had obtained the footage.
"These allegations against the national intelligence agency and this illegal operation is some kind of espionage activity. This paper is now involved in this espionage," Erdogan said, adding that he had instructed his lawyer to file a lawsuit.
The state-run Anadolu news agency said on Friday that the Istanbul chief prosecutor's office had launched an investigation into Cumhuriyet's editor-in-chief Can Dundar under counter-terrorism laws.
Dundar defended the newspaper's coverage on his Twitter account. "We are journalists, not civil servants. Our duty is not to hide the dirty secrets of the state but to hold those accountable on behalf of the people," he said in a tweet on Monday.