Hungary's prime minister has said he wants to debate the possible reintroduction of the death penalty with his European Union partners.
Viktor Orban said current penalties for serious crime were too lenient and capital punishment should be "kept on the agenda" in Hungary.
He raised the issue after the murder of a young tobacconist last week.
Austrian MEP Joerg Leichtfried said bringing back the death penalty would be "barbaric".
Mr Orban's Fidesz party has been coming under increasing pressure as it loses ground to the far-right Eurosceptic Jobbik party.
Last week a 21-year-old female shop assistant was murdered in the western town of Kaposvar. Her funeral was held on Wednesday.
The prime minister's comments have aroused controversy at home and abroad.
Fidesz, which has governed the country since 2010, is expected to face a strong challenge from Jobbik when elections are held in 2018.
Analysis: Nick Thorpe, BBC News, Budapest
Mr Orban's Fidesz, which has governed the country since 2010, is trying to compete with the radical nationalist Jobbik party, which has emerged as the main challenger to his rule.
Jobbik have long promised to restore capital punishment if they come to power - now a possibility - at the elections in 2018.
Another issue in Hungary is the scene of the crime - in a so-called National Tobacco Shop.
The sale of tobacco in Hungary has been limited since 2013 to such shops, the windows of which are blacked-out to prevent young people under the age of 18 seeing inside, and being encouraged to smoke.
A spate of attacks in such shops has provoked a public debate about the physical safety of assistants in shops that passers-by cannot see into. Some shop keepers have begun taking down the foil that covers the windows, in defiance of the law.
Other government politicians have made statements supporting and attacking the idea of the death penalty as a deterrent.
The leader of the Fidesz parliamentary group, Antal Rogan, said on state radio that he was aware that capital punishment was not permitted under EU rules.
But he said "a substantial debate can be raised [at] EU level" if a member state disagrees.
European Parliament President Martin Schulz said he would contact Mr Orban to discuss the issue.
The Council of Europe (CoE) said the return of the death penalty would be "contrary to the values that Europe stands for". Its human rights commissioner, Nils Muiznieks, expressed his concern and called on Hungary to pay more attention to human rights.
He also mentioned a controversial questionnaire launched by the Fidesz government last week, which openly links migration to terrorism, and blames EU policies for the current influx of illegal migrants.
Hungary banned the death penalty shortly after the fall of communism in 1990.