Rav Moshe Feinstein in a letter to the governor of New York wrote explaining that the strict requirements of Torah law limiting executions only applied historically in the limited case of a well ordered society. But there is a legitimate use of capital punishment to defend society – even where the Torah law is not fulfilled. A secular society has the right to protect itself.
Effectively, Reb Moshe is telling the governor that it is appropriate to use capital punishment in the United States even in cases that don’t meet the strict legal halachic requirements:
As a consequence of these two factors there were almost no Jewish murderers because of the awareness of the severity of the prohibition of murder and because they were educated by means of the Torah and the punishments of the Torah to understand the seriousness of the crime. They were not simply afraid of punishment in the sense of getting caught but were afraid of the crime itself.