Netanyahu rival Benny Gantz seeks support from PM's party to form government
"I would be the prime minister for the first two years," he said.
And if Netanyahu "is cleared (of any wrongdoing) he could return and become prime minister", Gantz added.
On Thursday, Attorney General Avichai Mandelblit announced he had charged Netanyahu with bribery, fraud and breach of trust, prompting speculation that the end of the premier's decade-long tenure was nigh.
The indictment came as Israel edged closer to its third general election in a year, after two inconclusive polls in April and September.
On Wednesday former army general Gantz, whose party gained one more seat than Likud in the September poll, said he was unable to form a government and secure a majority in the 120-seat Knesset, or parliament.
Gantz, leader of the centrist Blue and White coalition, was asked to form a government by President Reuven Rivlin after Netanyahu also failed to do so.
Netanyahu remains the country's interim premier, however.
Parliament now has less than three weeks to find a candidate who can gain the support of more than half of the Knesset's 120 lawmakers, or a deeply unpopular third election will be called.
Gantz, speaking in Tel Aviv, said his proposal was "the only alternative to holding new elections".
Under Israeli law, while ministers cannot remain in place after being indicted, a prime minister is not legally required to resign unless convicted and with any appeals processes exhausted.
In addition to the premiership, Netanyahu holds portfolios including agriculture and health, positions he may have to vacate in the coming days.
Netanyahu, the first Israeli prime minister to be indicted in office on corruption charges, has denounced a "coup" against him, dismissed the charges as "false" and "politically motivated" and vowed to hold onto power.
"What is going on here is an attempt to stage a coup against the prime minister," Netanyahu said.
"The object of the investigations was to oust the right wing from government."
In a 15-minute speech, Netanyahu railed against his political rivals and state institutions, accusing the police and judiciary of bias.
The veteran politician argued that it was time for an "investigation of the investigators".
He vowed to continue as prime minister despite potential court dates and intense political pressure.
"I will continue to lead this country, according to the letter of the law," he said. "I will not allow lies to win."
Political rival Benny Gantz, who had been trying to form a coalition government, said it was a "very sad" day for Israel to indict a leader, but called on Netanyahu to "step down from his position and focus on the charges against him".
"There is no coup in Israel, but rather those that have barricaded themselves in power," he said.
The 70-year-old premier, nicknamed "Mr Security" and "King Bibi", has been in power since 2009 and dominates Israel's political scene.
He may now ask the parliament, or Knesset, to grant him immunity from prosecution.