Israeli political landscape is crumbling as the deadline to form a coalition government approaches without any progress.
Netanyahu blamed Liberman for the failure to form a new government.
The decision triggers a fresh election, to be held on 17 September.
According to Israeli law, Netanyahu has 42 days to announce a new government.
The dramatic vote, less than two months after parliamentary elections, marked a setback for Netanyahu and left the longtime leader of the Jewish state's future in turmoil.
By Monday, one newspaper, Maariv, had already published a poll asking, "If elections were held today, who would you vote for?"
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Ultra-Orthodox parties consider conscription a taboo, fearing that military service will lead to immersion in secularism.
Whatever Liberman's intentions, he managed to seriously wound Prime Minister Netanyahu, who will be headed to his October 2 pre-indictment hearing without the benefit of a revised immunity law and without the override clause, which could cost him dearly.
"Unfortunately, I haven't been able to convince Lieberman to avoid another election", Netanyahu told reporters.
The letter's reference to a "reduction of the powers of the courts" comes amid ongoing reports that Netanyahu is working to include a "legal appendix" in his coalition agreement, which will allow the Knesset to "override" rulings by the Supreme Court.
"This is new for Israel", said Reuven Hazan, a politics professor at Hebrew University.
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Kahlon, however, expressed strong opposition to new elections, saying, "I very much hope that the prime minister will succeed in forming a government in the next 30 hours".
"If he can't form a government, he prefers to go to an election where he might fare better than before than have a situation where he won't be prime minister", said Gayil Talshir, a senior political science lecturer at Hebrew University of Jerusalem.
Reporting from West Jerusalem, Al Jazeera's Harry Fawcett said Netanyahu worked until the deadline but failed to find a formula that would have given him a majority in parliament.
Without the five seats of Mr Lieberman's Yisrael Beiteinu party, Mr Netanyahu can not muster a majority. They have accused Lieberman of betraying his voters and dragging the country to an unnecessary and expensive election campaign out of personal spite and jealousy of Netanyahu.
The Likud nevertheless won five more seats than last time, which Netanyahu took as a vote of confidence, and together with the right-wing and religious parties that made up his last coalition, seemed poised to form a government with a majority of 65 seats.
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