S&D group president Gianni Pittella and vice-president Victor Boştinaru said, in a joint statement, "Every day of ineffective actions means further victims. Every single day of shameful silence causes sufferings and destruction. What else are we waiting for?
"[The] EU must behave as a serious political actor by calling for an immediate ceasefire in the Gaza Strip and then lead a comprehensive peace conference on the Israeli-Palestinian conflict," they urged.
"[Catherine] Ashton's mandate has not yet expired," said the deputies. "The high representative must meet her responsibilities in this regard, as well as playing a meaningful role in the peace process in Gaza Strip war. There can be no excuse for the lack of EU political initiative.
"Every single day of shameful silence causes sufferings and destruction"-Gianni Pittella and Victor Boştinaru
"We support all international and regional efforts aiming to stop the ongoing violence in the Gaza Strip and in Israel.
They continued, "We condemn the continued firing of rockets by Palestinian militants into Israel. We also condemn the disproportionate use of force by the Israeli army in Gaza - an estimated 70 per cent of the more than 700 Palestinian victims are civilians, including many children - and we call for an end to this military operation through the de-escalation of the conflict.
"The longer we wait, the less room there is to achieve a rapid ceasefire and a final appeasement of this bloody conflict based on the two-state solution - with 1967 borders and Jerusalem as capital of both states - with the state of Israel and an independent, democratic, contiguous and viable Palestinian state living side-by-side in peace and security," they argued.
"The European Union was prepared to welcome the appointment of the new government of independent personalities following the Palestinian reconciliation, and that certainly puts us in a very different place to Israel, and of course we have offered again to reactivate the EU border assistance mission as part of any peace settlement.
In addition, they said, "I think above all, when [US secretary of state] John Kerry is talking about there being a long-term solution not just a ceasefire, and Europe is talking at the same time about the status quo being unsustainable, I still have to hope that European influence on this situation will not just achieve a ceasefire, although a ceasefire is absolutely necessary, but will achieve that within a context of trying to bring a long-term solution to the great humanitarian crisis that is Gaza."
Greens/EFA co-presidents Rebecca Harms and Philippe Lamberts agreed, saying, "The dramatic conflict in Gaza must stop immediately.
"We condemn the bombing and shelling of hospitals, schools, and other civilian areas, with the resulting deaths of a shocking number of Palestinian women and children, as reported by Human Rights Watch.
They explained, "These civilians can go nowhere in order to escape the violence as Gaza is under constant siege.
"The EU should look at all legal, economic and diplomatic means to exert influence in order to provide for a sufficiently rapid response"-Rebecca Harms and Philippe Lamberts
"There can be no justification for the disproportionate and continued violence against civilians in the most densely populated area of the world.
"The Israeli defence forces must immediately and fully respect international humanitarian law," argued the MEPs, adding, "We also condemn the continued firing of indiscriminate rockets into Israel by Hamas and other groups.
They also welcomed the "UN commission of inquiry concerned with all violations of international human rights law and international humanitarian law by all sides.
"The EU should look at all legal, economic and diplomatic means to exert influence in order to provide for a sufficiently rapid response.
"An immediate end to the situation on the ground must be accompanied by full and unhindered humanitarian access to the victims in Gaza," they concluded.
"I am worried that minds in Brussels are too turned towards the terrible events in Ukraine but that that has deflected some of the political attention Europe needs to be devoted to the Middle East"-Richard Howitt
Meanwhile, UK deputy Richard Howitt criticised Europe's "political will", saying, "I do not support a one sided text but I do deeply regret that led to the European Union member states abstaining on the call for an inquiry.
"If Israel is operating within international law under its right to self-defence, then frankly it should not have any fears about being open to an inquiry, and indeed as a member of the UN, it has a duty to do so.
But, he complained, "The truth is that the previous inquiry into alleged human rights abuses in the last Gaza conflict, the well-known Goldstone commission, found prima facie evidence of human rights violations but that the United Nations did not act upon it.
"It smacks of a failure of political will in Europe, as well as in the international community more generally, to uphold human rights and international humanitarian law in relation to Israel-Gaza," he said, concluding, "I am worried that minds in Brussels are too turned towards the terrible events in Ukraine but that that has deflected some of the political attention Europe needs to be devoted to the Middle East."