If the law comes into force, anyone deemed to have committed a "nationalistically motivated murder" could be sentenced to death, writes The Times of Israel.
In practice, this means that Palestinians imprisoned for murder in Israel can be executed. However, the law does not apply to Israelis who kill Palestinians.
The proposal will now undergo three rounds of voting, the first of which is reported to be possible as early as this week.
The Knesset's green light came after Gal Hirsch, Israel's coordinator on the hostage issue, stated that Prime Minister Benjamin Netanyahu supports the change in the law.
The bill was brought forward by the ultranationalist party Jewish Power (Otzma Yehudit), whose leader Itamar Ben-Gvir has long advocated for the death penalty.
"Every terrorist who intends to kill should know that there is only one possible punishment - death," Ben-Gvir, who is Israel's Minister of Internal Security, said on Monday, according to Haaretz.
