By Alissa de Carbonnel

STRASBOURG (Reuters) - The leaders of the European Parliament's two largest groups called on Tuesday for the European Union to halt membership talks with Turkey because of its post-coup purges.

"Our message to Turkey is very clear: accession negotiations should be frozen immediately," said Manfred Weber, the head of the largest faction in the European Parliament, the center-right European People's Party.

He was echoed by Gianni Pitella, the leader of the socialist group, the parliament's second biggest: "We want to freeze the accession talks."

More than 110,000 people in Turkey - including soldiers, academics, judges, journalists and Kurdish leaders - have been suspended from their positions or dismissed over their alleged backing for the plotters of a failed military coup in July.

Some 36,000 have been arrested and media outlets have been shut.

"Turkey under Mr Erdogan is more and more drifting towards an authoritarian regime," Pitella said, referring to Turkish President Tayyip Erdogan.

"Our political message towards Turkey is that human rights, civil rights, democracy are non negotiable if you want to be part of the EU.

Erdogan, exasperated with the EU's intensified criticism of his rights record, has said the bloc would have to "live with the consequences" should it stop the talks and that Ankara could instead join an security alliance run by Russia and China.

The post-coup crackdown has taken the EU aback, annulling a period of warmer tone between Turkey and the bloc, which had promised as recently as last March to speed up Ankara's accession talks in exchange for its help in keeping migrants away from European shores.

This cooperation, critical for the EU, is still going on but some in the EU worry it could eventually fall victim to the spiraling recriminations.

Erdogan, who blames the EU for not showing enough understanding for the gravity of the situation in Turkey, said he could put the EU talks to a national referendum next year.

Turkey still hopes to win visa-free travel to the EU but earlier promises of granting the privilege to Ankara by the end of the year now seem distant.

Among EU countries, Austria and Luxembourg have led calls to stop Turkey's membership talks, which have only made very limited progress over 11 years in any case.

But Germany, France and most of the other EU states for now back continued engagement and fear putting at risk Turkey's collaboration on migration.

All stress, however, that the talks would come to an end should Turkey reinstate the death penalty.

(Additional reporting by Tom Koerkemeier, writing by Gabriela Baczynska Editing by Jeremy Gaunt.)