"The coalition is stable, and no one, me or anyone else, has plans to go to elections", he declared in Tel Aviv. "We're going to continue to work together for the good of Israeli citizens until the end of the term in 2019".
Netanyahu, prime minister for a total of almost 12 years, addressed the nation as news of the recommendations broke, proclaiming his innocence and making clear he had no intention of resigning.
A prime minister facing such police recommendations or who has been formally charged is not obliged to resign.
Channels 10 and 2 TV and the Jerusalem Post and Haaretz newspapers reported police recommended indictments in both cases.
In a statement, police said there was sufficient evidence to indict Netanyahu in the first case, known as File 1000, for accepting bribes, fraud and breach of trust.
Lapid's remarks Wednesday came the morning after Israeli police recommended Netanyahu be indicted on bribery and breach of trust charges in two cases.
" I am certain, as I have always been certain, and nothing has changed, that the truth will come to light and nothing will come of this".
He accused police of being on a witch hunt and vowed to remain in office. Israeli media say Mr Netanyahu has been questioned by investigators at least seven times.
Benjamin Netanyahu's lawyer, Amit Hadad, says police recommendations of corruption charges against the prime minister are based on "false" statements.
A public debate has always been under way in Israel on whether Mandelblit, who has avoided interviews, might be reluctant to prosecute a sitting prime minister for the first time in Israeli history, especially one who promoted him through government ranks. In the Hadashot News poll, 48 percent of those polled said that Netanyahu should resign in the wake of the allegations, while 36 percent said he did not have to resign.
But he stressed Netanyahu is innocent until proven guilty and that he would wait for the attorney general's decision.
Lapid, who also called on Netanyahu to step down, was finance minister at the time one of the allegations took place.
He was chosen the Prime Minister of Israel in 2009.
"I was a member of Likud in 1999 when Netanyahu was an unpopular prime minister, but today he is very popular", he said.
Mr Netanyahu's ruling coalition, too, shows no signs of weakness.
The recommendations marked a dramatic ending to a months-long investigation into allegations that Netanyahu accepted gifts from Hollywood mogul Arnon Milchan and Australian billionaire James Packer, and suspicions that Netanyahu offered to give preferential treatment to a newspaper publisher in exchange for favourable coverage.
In contrast to Mr Olmert, who eventually stepped down and was convicted and imprisoned, Mr Netanyahu is still relatively popular with the public and enjoys broad political support in his Likud party and among coalition partners - almost all of whom stand to lose power if elections were held today.