A Philippine lawmaker filed an impeachment complaint against President Rodrigo Duterte on Thursday because of the thousands of deaths that have happened in his anti-drug crackdown and for alleged corruption, although the bid faces an uphill battle with Mr. Duterte’s allies holding an overwhelming majority in Congress.

Rep. Gary Alejano said the complaint he filed at the House of Representatives alleges Mr. Duterte violated the constitution and betrayed the public trust with his actions, including the crackdown that has sparked extrajudicial killings of drug suspects and because of a failure to declare huge bank deposits as required by law.

“We are of the firm belief that President Duterte is unfit to hold the highest office of the land and that impeachment is the legal and constitutional remedy to this situation,” said Mr. Alejano, who was accused of involvement in a failed coup attempt several years ago.

Although opposition lawmakers lack the numbers to impeach Mr. Duterte, Mr. Alejano said there was a need to stop his “excesses and crimes.” More than 260 of the 292 House members belong to a pro-Duterte bloc.

“Around 8,000 have been killed already,” Mr. Alejano said, referring to the estimated number of mostly drug suspects killed in the crackdown Mr. Duterte launched after taking office last June.

Presidential spokesman Ernesto Abella suggested the impeachment bid and opposition criticism were possible efforts to destabilize the Duterte administration.

Mr. Alejano’s complaint cited Mr. Duterte’s speeches, where he threatened drug lords with death and encouraged law enforcers and civilians to shoot drug suspects if they fight back, and recent Senate testimony by retired police officer Arturo Lascanas and a former militiaman Edgar Motabato, who said they were members of a death squad under Mr. Duterte when he was mayor of southern Davao city.

Mr. Lascanas and Mr. Matobato separately testified they were involved in hundreds of killings of drug suspects and political opponents of Mr. Duterte in Davao. Mr. Duterte has denied he condoned extrajudicial killings.

Mr. Duterte has not responded in detail to the allegations, and his allies have questioned the credibility of the two men.

Mr. Alejano’s complaint also cited accusations by opposition Senator Antonio Trillanes IV, who accused Mr. Duterte of failing to declare more than 2 billion pesos ($40 million) in bank deposits as required by law. Mr. Duterte has denied any wrongdoing.