The UK government has come under rising pressure from MPs to start making contact with Palestinian group Hamas.
A Foreign Affairs Committee report also said it was "regrettable" UK-supplied military items were "almost certainly" used by Israel in the Gaza conflict.
The cross-party group, which monitors foreign policy, called on the EU to make relations with Israel conditional on its peace-making efforts.
Hamas was also criticised for its use of rockets on Israeli civilian targets.
But committee chairman Michael Gapes said the committee saw "few signs that the current policy of non-engagement with Hamas" was effective.
He added that the government "should urgently consider engaging with moderate elements within Hamas" as it had with the political wing of Hezbollah in Lebanon earlier this year.
The wide-ranging report condemns Israel for the continuing growth of settlements and for its blockades around the Hamas-controlled Gaza strip.
It was unacceptable, said Mr Gapes, to deny unrestricted access for humanitarian assistance.
And the report also called for the Foreign and Commonwealth Office to declare whether it considered war crimes had been committed during the December 2008 to January 2009 conflict in Gaza and southern Israel.
Hamas came into criticism for its rocket attacks, but MPs concluded that Israel's military action in Gaza was "disproportionate".
Mr Gapes said: "Rocket fire from Gaza by Hamas and other Palestinian groups on civilian targets in Israel is unacceptable.
"It generates the risk of a renewed escalation in violence, and constitutes a central obstacle in the way of Israeli willingness to move forward towards a two-state settlement."
The report welcomed the endorsement by the Israeli Prime Minister Benjamin Netanyahu of a two-state solution to the conflict.
The committee added that the split between Hamas in Gaza and the Palestinian Authority in the West Bank was a central obstacle to creating a united and democratic Palestinian state, and called for elections that could be accepted by all parties.
Former prime minister Tony Blair, who is now a Middle East peace envoy, was commended for "making an important contribution to Palestinian economic and institutional development".
But movement, access and administrative restrictions on the West Bank continued to represent a "major obstacle to further Palestinian economic development," it added.
Hamas takes its name from the Arabic initials for the Islamic Resistance Movement.
Designated a terrorist organisation by Israel, the US and the EU, it is seen by its supporters as a legitimate fighting force defending Palestinians from a brutal military occupation.