But our correspondent says the question is whether the White House regards this as sufficient to make up for the lack of movement on the issue of Jewish settlements in the occupied West Bank.
In his keynote Mid-East speech in Cairo on 4 June Mr Obama stressed that he wanted all settlement activity to stop.
But in his speech at Bar-Ilan university Mr Netanyahu said settlers were not "enemies of peace" and did not move from his position of backing "natural growth" in existing settlements.
The Israeli leader offered to talk to the Palestinians immediately and with "no preconditions".
Tim Franks, BBC News, Jerusalem
Benjamin Netanyahu has shifted. He has used the word "state", when it comes to Palestinian self-rule.
In another deeper sense, though, there has been no shift. Mr Netanyahu's closest aides have been saying for months that they have two over-arching pre-conditions: a public Palestinian acceptance of Israel as the nation-state of the Jewish people, and a complete demilitarisation of any future Palestinian entity.
And Mr Netanyahu tersely dismissed the US call for an end to settlement expansion: these people have to live, he said. He described them as "pioneers" and "principled".
This is a speech which will shore up the prime minister's position within his right-wing coalition. It is, whatever you think of the rights and wrongs of it, a powerful forehand deep into the back court of the Americans. It will be fascinating to see when and how the Americans return the ball.
"We want to live with you in peace as good neighbours," he said.
Mr Netanyahu also said he was willing to go to Damascus, Riyadh and Beirut in pursuit of a Middle East peace deal.
He went on to tackle the major stumbling blocks in negotiations with Palestinians over the years.
Not least was the issue of Palestinian refugees who fled or were forced from their homes in what is now Israel in 1948 and 1949.
The Palestinians say they and their millions of descendants have the right to return to Israel - which would mean an end to its Jewish majority - but Israel has consistently rebuffed that demand.
Mr Netanyahu stuck to a similar line, saying: "The Palestinian refugee problem must be resolved outside the borders of the state of Israel.
"Any demand to resettle refugees within Israel undermines Israel as a state for the Jewish people."
Another key issue the two sides have failed to agree on is the status of Jerusalem.
Mr Netanyahu insisted the city must be the "united capital of Israel", although Palestinians want it divided to allow them to locate the capital of a future state there.
'Racist and extremist'
Agreeing the principle of a Palestinian state, he said Israel would "be prepared for a true peace agreement [and] to reach a solution of a demilitarised Palestinian state alongside the Jewish state".
But only if "we receive this guarantee for demilitarisation and the security arrangements required by Israel, and if the Palestinians recognise Israel as the nation of the Jewish people".
Correspondents say even with the provisos Mr Netanyahu has added, his comments on a Palestinian state are sure to anger many in his own coalition.
Nabil Abu Rdainah, a spokesman for Palestinian Authority President Mahmoud Abbas, said the Israeli leader's speech "torpedoes all peace initiatives in the region".
Another Abbas aide, Yasser Abed Rabbo, told the AFP news agency that recognition of Israel's Jewish character was a demand for Palestinians "to become part of the global Zionist movement".
The militant Hamas movement, which controls the Gaza Strip, said the speech reflected Mr Netanyahu's "racist and extremist ideology".
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