ANKARA, Oct 10 (Reuters) - Turkish authorities on Thursday started investigations into leaders of the pro-Kurdish opposition and detained 21 people for criticising the military offensive against a Kurdish militia in northeast Syria, state-owned Anadolu news agency said.

Turkey launched the incursion against the Kurdish YPG militia on Wednesday after a withdrawal by U.S. forces with whom ther were allied. Ankara deems the YPG a terrorist group over links to PKK militants who have fought a decades-old insurgency in Turkey.

While most of Turkey’s opposition parties have voiced support for the operation, the pro-Kurdish Peoples’ Democratic Party (HDP) has called for the offensive to stop, saying it is an “invasion attempt”.

HDP co-leader Sezai Temelli said on Wednesday the operation was an attempt by the government to drum up support amid declining public backing.

Prosecutors launched an investigation against Temelli and HDP’s other co-leader, Pervin Buldan, over their remarks about the offensive, Anadolu said.

It said Temelli and Buldan were accused of “carrying out propaganda for a terrorist organisation” and “openly insulting Turkey’s government”.

Three other HDP lawmakers are being investigated over similar charges, the news agency said.

The government accuses the HDP of ties to the Kurdistan Workers Party (PKK) militant group and thousands of its members have been prosecuted for the same reason, including its leaders. The HDP denies such links.

Hours after the operation started on Wednesday, authorities also launched investigations against 78 individuals who criticised the offensive on social media, Anadolu said.

On Thursday, 21 people were detained in the southern province of Mardin for their social media posts.

The suspects are accused of “provoking the public to hatred and animosity” and “carrying out propaganda for a terrorist organisation”, it said.

Turkish authorities have launched similar investigations after each of its two previous cross-border operations into Syria. More than 300 people were detained for social media posts criticising Turkey’s offensive into northern Syria in January 2018. (Reporting by Tuvan Gumrukcu; Editing by Daren Butler and Angus MacSwan)