Prime Minister Aso is a Roman Catholic
Japan has hanged two convicted murderers, including one who strangled two schoolgirls with his bare hands.
The latest executions bring the total number of death penalties implemented this year to 15, thought to be the highest total in many years.
Last year, Japan executed nine convicted killers.
Japan is one of the few countries in Asia which has stepped up its use of the death penalty, despite international condemnation.
The two people hanged on Tuesday were Michitoshi Kuma, 70, and Masahiro Takashio, 55, the justice ministry said in a statement.
Kuma kidnapped two seven-year-old girls on their way to school in southern Japan in February 1992 and strangled them, dumping their bodies in the mountains.
Takashio was convicted of breaking into a house in northern Japan in March 2004 and stabbing a 55-year-old woman and her 83-year-old mother to death before stealing 50,000 yen, or about $500.
"Both crimes stemmed from cruel motives and took the precious lives of victims," Justice Minister Eisuke Mori told reporters.
Three people were executed in September.
Executions are not announced beforehand and are carried out in secret, usually with strong local support.
Japanese media reported that Japan had a de facto moratorium on executions for 15 months until 2006 because the then Justice Minister, Seiken Sugiura, said the death penalty went against his Buddhist beliefs.
It also noted that Mr Taro Aso, who took office as prime minister on September 24, is a member of Japan's small Roman Catholic community.
The Roman Catholic Church opposes capital punishment.
Amnesty International has called on Japan to impose an immediate moratorium on the use of the death penalty.
It notes that United Nations reviews of human rights in Japan have expressed particular concern about Japan's use of the death penalty.
Amnesty describes the death penalty as "the ultimate denial of human rights", saying that it is "the premeditated and cold-blooded killings of a human being by the state", which is "cruel, inhuman and degrading".
But while rights groups decry the use of the death penalty, without exception, public opinion in Japan seems to support its continued use.
It is thought that about 100 convicted murderers and others on death-row are awaiting execution.