SEOUL - South Korea's Kakao Mobility on Tuesday said it would re-enter talks over its proposed car-sharing service with an open mind, and would even consider abandoning the idea, should taxi drivers who protested the service return to negotiations.

The transportation unit of Kakao Corp, operator of the country's most popular chat app, also said it has decided to halt trials of the car-sharing service.

The comments come after the firm's appeal to car owners sparked a series of mass demonstrations with taxi drivers complaining the service would destroy their livelihoods. Two protesters died in separate incidents by self-immolation.

Lawmakers have called on drivers unions to meet the firm and government officials to reach a consensus. The unions boycotted the talks as trials continued after the first death.

"Without any strings attached, we will join the dialogue with an open mind, and from a stance where even scrapping the launch is a possibility," Kakao Mobility said in a statement.

South Korea has one of the world's highest smartphone penetration rates, yet app-based ride-hailing services have struggled in the face of strong unions and tight regulation. 

Kakao Mobility also runs a cab-hailing service connecting taxi drivers and passengers.

Lee Yong-bok of the Korea National Joint Conference of Taxi Association said Kakao Mobility should have stopped the trial earlier if it really wanted to talk.

"We are asking the transport minister to resign," Lee told Reuters. "The ministry, and the ruling party: They have to show us something to make us believe they want to have discussions from a clean slate and not take Kakao Mobility's side."

(Reporting by Ju-min Park; Editing by Christopher Cushing) ((ju-min.park@thomsonreuters.com; +82 2 3704 5650; Reuters Messaging: ju-min.park.thomsonreuters.com@reuters.net))