"What I'm afraid of is that on one side the lack of process is in itself something that is deteriorating the situation," the EU's Federica Mogherini said.
"But on the other side, I'm also worried about the fact that a process that has gone on for so long, if we just restart the process and that's it, it might not be enough."
Speaking at the Brookings Institution, Mogherini suggested one way forward would be to enlarge the Middle East Quartet steering the negotiations.
Set up in Madrid in 2002, the body is composed of the United Nations, the United States, the European Union and Russia. Former British prime minister Tony Blair acts as its special envoy in mediating a peace deal between the two sides.
"The sense of frustration, the lack of hope, is so strong on both sides, that we need not only to restart the process but ... make sure that the process brings some immediate concrete results," Mogherini said.
US top diplomat John Kerry spent the early part of last year shuttling between Israel and the Palestinian territories trying to reach a long-elusive deal, before his bid collapsed in acrimony in April.
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"We need to build this international frame and restructure it more to restart the efforts that John Kerry was very well doing last year," Mogherini said.
Enlarging the Quartet "could be helpful" as it would it enable talks on not just the Israeli-Palestinian conflict but also the broader Arab-Israeli conflict.
There could be "an opportunity to work on a common security basis in the region between Israel and some of the Arab countries," she said, highlighting the role played by Egypt in ending the Gaza war last year.
Arab countries were also playing a "positive role" in fighting militants from the Islamic State group, so that could bring an "added value to enlarge the scope of the" peace process, Mogherini said.
She stressed however that it was so far only being thought about, adding "it's not for the coming weeks."
Later, the envoys could "maybe start preparing the framework for what could be done in a couple of months time, hopefully."
Envoys from the United States, the European Union, the United Nations and Russia are to meet later this month to discuss the next steps to address the Israeli-Palestinian crisis.
The gathering of the Middle East diplomatic quartet will take place January 26 in Brussels to discuss ways of reviving the peace process after the Palestinians failed to win UN Security Council approval of a resolution on ending the Israeli occupation.