The bill was rejected in a 52-58 vote on Monday, Israeli newspaper Yedioth Ahronoth said.
The legislation, whose validity has been extended every five years since 1967 and which will expire at the end of June, will be put to a vote in the coming weeks one more time, the report said.
There are reportedly concerns in Israel that the new government crisis may result in yet another early elections, which the country has already had four times in a row in two years. In March, a snap election resulted in a coalition relying upon a minimum parliamentary majority of 61 votes in the 120-seat Knesset.
In April, Idit Silman withdrew from the coalition, which she chaired, leaving it without a majority in parliament, and joined the opposition.
Last June, the leader of the right-wing Yamina political alliance, Naftali Bennett, was elected the prime minister of Israel. Yair Lapid, the head of Israel's largest opposition party Yesh Atid, will replace him in 2023, under an agreement on a rotation government.