In a statement, the prime minister said he had worked “tirelessly” to establish a unity government with his chief rival, former military chief Benny Gantz, but been repeatedly rebuffed.
Facing a Wednesday deadline, Mr Netanyahu said he was returning the “mandate” to President Reuven Rivlin, who will now ask Mr Gantz to try to form a coalition.
While Mr Netanyahu remains at the helm of his Likud party, his announcement marked the second time this year he has been unable to form a government.
I have worked tirelessly both in public and behind the scenes to establish a broad, national unity government
With Israel’s attorney general set to decide in the coming weeks on whether to indict Mr Netanyahu in a series of corruption cases, the longtime Israeli leader could come under heavy pressure to step aside.
In last month’s national election, he fell short of securing a 61-seat parliamentary majority, but Mr Rivlin gave him the first opportunity to form a government because he had more support — 55 seats — than Mr Gantz with 54.
Mr Netanyahu had hoped to form a broad “unity” government with Mr Gantz, who heads the centrist Blue and White party, but the PM insisted his coalition include his traditional allies, a collection of hardline and religious parties, drawing accusations from Mr Gantz that he was not negotiating in good faith.
“Since I received the mandate, I have worked tirelessly both in public and behind the scenes to establish a broad, national unity government. That’s what the people want,” Mr Netanyahu said in a statement.
“During the past few weeks, I made every effort to bring Benny Gantz to the negotiating table. Every effort to establish a broad national unity government, every effort to prevent another election,” he said. “To my regret, time after time he declined. He simply refused.”
In a short statement, Mr Gantz’s Blue and White party said: “Now is the time of action.”
“Blue and White is determined to form the liberal unity government, led by Benny Gantz, that the people of Israel voted for a month ago,” it said.
There is no guarantee that he will succeed. He has expressed willingness to form a partnership with Likud, but not if Mr Netanyahu continues to lead while he faces such serious legal problems. For the time being, Likud has remained behind its leader.
Without Likud, Mr Gantz will have a hard time securing a majority in parliament. The opposition to Mr Netanyahu includes a diverse group, ranging from Arab parties to the secular ultra-nationalist party Yisrael Beitenu, that are unlikely to sit together in partnership.
If Mr Gantz fails during his 28-day window, a majority of legislators could try to endorse a third candidate, something that has never happened before, and if that fails, the country would be forced into the unprecedented scenario of a third election in under a year.