There are currently 42 prisoners on death row in Taiwan. (Representational)

Taiwan executed a death-row inmate on Friday, the first execution carried out under President Tsai Ing-wen's government and despite ongoing calls from rights groups to abolish the death penalty.

Lee Hung-chi was executed at a jail in southern Kaohsiung city Friday afternoon by firing squad, according to the justice ministry, for killing his ex-wife and five-year-old daughter in 2014.

Lee stabbed his ex-wife to death outside the kindergarten their two daughters attended and then took one of the girls to his car, where he attempted to commit suicide by carbon monoxide poisoning.

Lee survived after they were rescued but the girl died two months later despite treatment.

"His actions were brutal and ruthless ... and inflicted irrepairable harms to the victims' families," deputy justice minister Chen Ming-tang told reporters, adding that the court had ruled there was no likelihood of Lee reforming.

Taiwan resumed capital punishment in 2010 after a five-year hiatus, with the death penalty reserved for the most serious crimes such as aggravated murder and kidnapping.

Some politicians and rights groups have called for its abolition, but various opinion surveys show majority support for the death penalty.

Chen said the government was gradually decreasing its use, but would not abolish it for now.

"Abolishing death sentence is an international trend and a long-term goal for the justice ministry ... but there is no consensus in our country," Chen said.

There are currently 42 prisoners on death row in Taiwan.

Lee's execution was the first since a former college student was put to death in May 2016 for killing four people in a random stabbing spree on a subway that shocked the generally peaceful island.

In 2012 the murder of a young boy in a playground reignited debate over the death penalty, after the suspect reportedly said he was anticipating free board and lodging in jail and would get a life sentence at most even if he were to kill two or three people.