TEL AVIV (Reuters) - Israeli right-winger Benjamin Netanyahu and centrist Tzipi Livni met Friday but failed to agree on forming a coalition government and left it unclear whether negotiations between their parties would continue.

After meeting for over an hour in Tel Aviv, each came out and blamed the other for lacking the will to compromise and form a broad-based, national unity government. Livni indicated her disappointment with Netanyahu's skeptical approach to peace talks with the Palestinians, which she has led since 2007.

However, neither ruled out further coalition negotiations.

Though outgoing Foreign Minister Livni's Kadima party won a February 10 parliamentary election by one seat from Netanyahu's Likud, neither controls even a quarter of the 120-seat Knesset. The president nominated the latter to try to form a government, on the basis that the new parliament has a right-wing majority.

Netanyahu still has over a month to form a government and has made clear that, while he can do so with right-wing parties, he would prefer a broader administration with the centrists.

Livni said Friday's meeting, held a week after Netanyahu was nominated for the premiership, ended without agreement on matters her party found fundamental. Among these, Livni has stressed her desire to negotiate for a Palestinian state, something Netanyahu has said is less of a priority for Likud.

Livni said, A two-state solution is not simply a hollow slogan -- it is the only way in which Israel can remain a democratic, Jewish state and it is the only way in which it can enlist an international coalition that will allow it to act and to confront the Iranian threat and terrorism.

Netanyahu said he was prepared to make major concessions to Livni. It is clear to all of us that a unity government will force compromises from both sides, he said. I would have been prepared to go a very long way toward unity.

Netanyahu said he told Livni he intended to continue peace talks with the Palestinians, but did not specify his approach. He has said in the past he will focus on bolstering the economy of the Israeli-occupied West Bank and is keen to set limits on the powers of any Palestinian state before it is established.

(Writing by Ori Lewis; Editing by Louise Ireland and Alastair Macdonald)

Israel