MEPs will hold a symbolic vote in December, following resolutions passed by the British and Spanish parliaments, and an official decision to recognise Palestine by the Swedish government.
France's National Assembly is set to vote on a non-binding resolution on December 2.
The Middle East process restarted in July 2013 but has been on hold since April, with tensions and violence mounting again dramatically in recent weeks.
"The sense of urgency is getting higher and higher in the absence of a political context," Mogherini told lawmakers at the start of what she said was a "timely" debate.
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"There has to be a direct dialogue."
The former Italian foreign minister, who has taken over as diplomatic chief of the 28-nation European Union, said the bloc was ready to "play a role" in moving the peace process forward.
She also reiterated her support for a two-state solution to resolve the crisis.
The European Parliament was initially due to vote on Thursday on the motion to recognise a Palestinian state but it was postponed until December at the last minute.
There has been international alarm over a spate of violent attacks in east Jerusalem and the deadlock over peace talks that are fuelling fear of another flareup after the war in Gaza earlier this year.