The bill, approved 52-49, would ease the requirements military courts must meet to sentence those convicted of "terrorist" crimes to death. Israel has not carried out any executions since 1962.
Prime Minister Benjamin Netanyahu voted in favour of the legislation, saying it was necessary in extreme cases. It requires three more votes in parliament to become law.
As the law stands now, a panel of three military judges must unanimously approve any death penalty in military courts.
The bill, put forward at the initiative of Defence Minister Avigdor Lieberman, would change the requirement to a majority instead of unanimity.
Palestinians in the occupied West Bank face military courts when arrested by Israel.
Israel abolished the use of capital punishment for murder in civil courts in 1954, though it can still in theory be applied for war crimes, crimes against humanity, genocide, treason, and crimes against the Jewish people.
In July as Netanyahu visited with family members of three Israelis stabbed to death by a Palestinian, he expressed support for the death penalty in certain cases.
"The death penalty for terrorists –- it's time to implement it in severe cases," he said while speaking with the family members.
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