The Communist country decided in 2011 to switch from firing squads to legal injection on humanitarian grounds, reportedly because of the trauma caused to the shooters. But it had been unable to execute anyone because the European Union bans factories from exporting drugs.
The country amended laws this year allowing the production of local chemicals to be used in executions, but the source of the drugs used in Tuesday's execution was unclear.
Thanh Nien daily reported that Nguyen Anh Tuan, a 27-year-old man condemned to death in 2010 for murdering a woman, was executed in a Hanoi prison on today.
Amnesty International said it was saddened to hear of the resumption of executions.
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"We regret that authorities in Vietnam have exercised the opportunity to review the death penalty in line with debates in other Southeast Asian countries," said Chiara Sangiorgo, the group's campaigner against the death penalty. "Instead of devising a better way of execution, they could have concentrated their efforts in launching a national debate with a view to abolition."
Vietnam allows for the death penalty for 21 crimes including drug smuggling, embezzlement, treason and subversion.
He said the EU had hoped difficulties in sourcing the chemicals might have triggered a moratorium on the death penalty in the country.
Vietnam, a one-party-ruled state that routinely sentences government critics to long prison terms, is under considerable international pressure to improve its human rights record, which most observers say has gotten worse over the last two years.
The EU considers the death penalty a human rights issue, unlike the United States.