Turkish authorities have detained 24 people on suspicion of disseminating "terror propaganda" against Turkey's military operation inside Syria, the interior ministry said on Monday.

The suspects are being held in a nationwide crackdown on those posting social media messages deemed to be supportive of terror groups, the state-run Anadolu news agency said.

The arrests come after President Recep Tayyip Erdogan urged national unity over the operation, in which one Turkish soldier was killed on Monday, warning those who respond to calls for protests will have to pay a "heavy price".

Those detained are accused of making propaganda for the Syrian Kurdish Peoples' Protection Units (YPG) militia deemed a terror group by Ankara and the target of Turkey's operation.

The Dogan news agency said investigations had been opened against a total of 57 people. Reports said that arrests took place in Istanbul and the Kurdish-majority city of Diyarbakir.

According to the agency and Human Rights Watch (HRW), 30 people were detained in Diyarbakir over their social media postings.

Among those taken into custody was writer and human rights activist Nurcan Baysal at her house late on Sunday, HRW said in a statement.

Baysal was detained in connection with her tweets calling for peace and condemning Ankara's offensive, the New York-based rights group said late on Monday quoting her lawyer.

Emma Sinclair-Webb of HRW said that "nothing in Baysal's tweets advocates violence", adding that she had long advocated for dialogue to end the decades long conflict between the Turkish state and the outlawed Kurdistan Workers’ Party (PKK).

"The move against people who took to Twitter shows that Turkey's government is determined to censor critical voices," Sinclair-Webb added.

- Probe into pro-Kurd MPs -

Turkey views the YPG militia as "terrorists" linked to the PKK, which has fought against the Turkish state since 1984 and is designated as a terror group not just by Ankara but also its Western allies.

It is seeking to root out the YPG from its western enclave of Afrin in Syria close to the Turkish border.

Turkish prosecutors have launched an investigation into unverified photos shared on social media claimed to have been taken in Afrin, purportedly showing that the offensive inflicted civilian injuries, TRT state broadcaster reported.

Prosecutors in the eastern Van province launched an investigation into four lawmakers from the pro-Kurdish Peoples' Democratic Party (HDP) who on social media urged people to take to the streets, TRT added.

Authorities are also probing social media posts of another HDP lawmaker Alican Onlu, according to the broadcaster.

Turkish anti-riot police on Sunday blocked protests in Istanbul and in Diyarbakir against Ankara's military operation inside Syria.

The rallies had been called by the HDP, whose members are facing a series of legal challenges for alleged ties with the PKK.

The Ankara governor on Monday said that while the military operation was underway, demonstrations could not take place in the capital without the governorate's permission.

Turkish authorities have in the last years strongly cracked down on social media posts deemed supportive of "terror", prompting concern from some activists that freedom of expression was being damaged.