Allegations about Israeli or Hamas abuses during the conflict in Gaza need to be investigated, David Miliband told MPs today.

In a statement on the Gaza crisis, the foreign secretary said more than 800 Palestinians had been killed, "apparently 250 of them children – the most terrible statistic of all".

He reiterated the government's demands for an immediate ceasefire and said allegations of war crimes needed to be properly investigated.

"Extremely serious allegations about the conduct of both sides have been made by the International Committee of the Red Cross and others," he said. "These allegations must be properly investigated."

Miliband said Britain wanted the UN to produce a "loud, clear, unified" message and that this was achieved when the security council passed a resolution last week demanding an immediate ceasefire.

He did not comment on the US decision to abstain when the security council voted.

However, the resolution was followed "within hours by its rejection by both sides of the conflict", he said.

Miliband spelled out three priorities for the international community. First, he said, relief was needed for the "desperate humanitarian situation" in Gaza. Britain had already increased its aid budget by $10m (£6.7m) since the conflict began, he added.

"The international aid agencies need the wholehearted cooperation of the Israeli government. I urge the Israeli government to provide it," he said.

Secondly, there had to be "security improvements, above all a curb on the trafficking of illegal arms in to Gaza".

Thirdly, there had to be "a political imperative to re-establish the unity of the Palestinian people under the leadership of the Palestinian Authority".

Miliband said the Israelis had argued against last week's UN security council resolution on the grounds that it could not accept an equivalence between a democratic state and a terrorist organisation.

"There is and can be no equivalence. Hamas have shown themselves over a number of years ready to be murderous in word and deed. Their motif is 'resistance' and their method includes terrorism," Miliband said.

"Israel is meanwhile a thriving, democratic state with independent judiciary."

"But one consequence of the distinction between a democratic government and a terrorist organisation is that democratic governments are held to significantly higher standards, notably by their own people.

"That is one reason we supported Resolution 1860 – to uphold the standards on which Israel and the rest of us depend.

"As a beacon of democracy in the Middle East, Israel's best defence is to show leadership in finding a political solution to this crisis and to comply with the standards of international humanitarian law."

Miliband continued: "Peace benefits Israelis and Palestinians; war kills both. They are destined to live next door to each other.

"They can either do so as combatants or as neighbours. We are committed to help them do the latter. That is what Israelis need and Palestinians need – it's also what we need – before it is too late."

The foreign secretary's statement did not spell out which allegations he wanted to see investigated, although the Hamas rocket attacks on Israel and Israeli responses resulting in the deaths of civilians have been condemned as breaches of humanitarian law.