"I have already passed on the message through quiet channels and I am now saying it in public," he said in a live televised address.
But his offer was immediately rejected by Palestinian chief negotiator Saeb Erakat, who told AFP the issue was completely unrelated to the crisis in the US-brokered peace talks.
"This order has nothing to do with the peace process or with the obligations that Israel has not implemented," Erakat told AFP by phone from Amman, Jordan. "This is completely rejected."
Direct peace negotiations between Israel and the Palestinians began on September 2 but ground to a halt two weeks ago after the expiry of a partial 10-month moratorium on Jewish settlement building.
Despite huge diplomatic pressure to reimpose the freeze, especially from the United States, Netanyahu has refused to do so, instead urging the Palestinians not to abandon the talks.
Palestinian president Mahmud Abbas has said he will not continue the talks unless Israel halts all settlement activity.
The Cairo-based Arab League backed him on Friday, but also gave Washington one month to try to resolve the impasse.
Around 50 Israeli right-wingers protested outside the American embassy in Tel Aviv on Monday night, throwing shoes and eggs at a poster of US President Barack Obama in protest at US pressure to halt Jewish settlements.
They shouted anti-Obama slogans and brandished placards, one of which read: "Obama, Israel is not ketchup so don't squeeze."
Recognition of Israel as a Jewish state has never been one of the core issues for resolving the conflict, but since Netanyahu came to power in 2009, it has become one of his key demands in any peace deal with the Palestinians.
"I'm not setting this as a condition for talks," he said on Monday. "But there is no doubt that such a step on the part of the Palestinian Authority would represent a confidence-building measure which would open a new horizon of hope and also trust."
The Palestinians formally recognised Israel as a state on the eve of the 1993 Oslo Accords, but have rejected the demand to recognise its Jewish character because that would amount to an effective renunciation of their cherished right of return for refugees from the 1948 Arab-Israeli war.
"What could convince the government, and more so the citizens of Israel, that the Palestinians are truly ready to live with us in peace?" Netanyahu asked rhetorically.
"Something that would signal a real change on the Palestinian side?"
Earlier, the Israeli government endorsed a bill mandating that a national referendum be held before any withdrawal from occupied east Jerusalem or the Golan Heights, the justice ministry said.
Both territories were later annexed by Israel after being seized in the 1967 Middle East war.
The measure must still pass three readings in parliament, although with the government's support, its passage into law is greatly eased.
Defence Minister and Labour party leader Ehud Barak, who has been under fire from members of his own party for being too accommodating towards Netanyahu, called Monday's decision an obstacle to peace.
"The referendum bill in the form in which it was passed today... raises question marks regarding the government's willingness and ability to advance a peace process," he said in a statement.
"The government must do everything possible to remove from the road the obstacle it has placed there today," he added.