The Ankara chief prosecutor's office opened the probe against Republican People's Party (CHP) MP Bulent Tezcan over charges of "insulting the president", Hurriyet daily said, following a complaint filed by Erdogan's lawyer Huseyin Aydin.
The charges are punishable by up to four years in prison.
Tezcan made the comments during a visit to the northwestern province of Tekirdag in support of a district mayor who is also being investigated over charges of insulting the president.
"What did the district mayor apparently say, he said 'fascist dictator'. Who did he apparently say it to? The (ruling Justice and Development) AK Party leader Erdogan. I don't know if the mayor said this or not.
Erdogan's spokesman Ibrahim Kalin described Tezcan's remarks as "hateful" on Twitter late Monday, adding: "This isn't politics, this is animosity against the people's will."
Meanwhile, Prime Minister Binali Yildirim described the MP's remarks as "impertinent" on Tuesday during a televised speech to his ruling party in Ankara.
A similar investigation was launched in 2016 against CHP leader Kemal Kilicdaroglu after he repeatedly called Erdogan a "tinpot dictator".
Speaking to AFP, Tezcan insisted that he had committed no crime with his words.
"No serious judicial system can regard this type of political criticism as a crime," the CHP spokesman said, vowing to fight on.
The CHP has repeatedly denounced an authoritarian drift under Erdogan, especially criticising the crackdown launched after last year's failed coup.
Over 50,000 people have been arrested since last July over alleged links to US-based Muslim cleric Fethullah Gulen blamed for the 2016 attempted putsch.
Others caught up in the crackdown include pro-Kurdish party MPs and journalists.
Another CHP MP Enis Berberoglu is currently in jail awaiting a new trial on charges of revealing state secrets and espionage.
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