Egypt says it has opened its border crossing with Gaza to allow the most critical casualties of Israeli airstrikes access to Egyptian medical care, following accusations that it has abandoned its usual role of mediating between the Israeli and Palestinian leaderships.

The opening of the border accompanied statements by Egyptian officials that stressed Egypt's active role in bringing the latest Gaza conflict, which Palestinians say has killed over 70 Gazans, to an end.

The spokesman for Egypt's foreign ministry, Badr Abdelatty, told the Guardian: "We have extensive and full contact with all parties concerned, either directly or internationally. Our main objective is to stop Israeli aggression. We are in full contact and pushing very hard to provide all humanitarian assistance to the Palestinians in Gaza."

Abdelatty's comments followed statements from the office of Egypt's president, Abdel Fatah al-Sisi, that he was communicating with key international figures – including the Palestinian president, Mahmoud Abbas, and the UN secretary general, Ban Ki-moon.

These interventions come amid accusations from Hamas officials that Egypt is no longer active in behind-the-scenes negotiations – claims given greater credibility by the political direction Egypt has taken in recent months.

When fighting broke out in Gaza in 2012, Egypt's then president, Mohamed Morsi – a member of the Muslim Brotherhood, a key ally of Hamas – won international acclaim for helping to broker a swift peace deal.

But since Sisi ousted Morsi last July, relations between Egypt and Hamas have significantly soured. Egypt has blocked most of the tunnels connecting Egypt and Gaza, while Hamas has been banned inside Egypt, its actions vilified in Egyptian media, and some of its members tried in absentia on charges relating to the Muslim Brotherhood.

"We don't have a relationship with Hamas," one senior military official told the Guardian in April. "We see them as a terrorist organisation that is allied to the Muslim Brotherhood."

But observers said Egypt was likely to still be communicating with both Hamas and Israel, even if its relationship with the former is strained. According to Issandr el-Amrani, a Cairo-based analyst, and project director for the Crisis Group's North Africa project, the links between Egyptian intelligence and Hamas continue.

"Even if they've been lower level in the past months, the link was never severed," said Amrani. "Egypt does not want to empower Hamas but that doesn't mean they want the conflict to go on … If that was the case two or three days ago, it isn't now."

Egyptians' ability to affect change is ultimately dependent on the receptiveness of both warring parties, Amrani said, while Egypt's current influence on Hamas is clearly less than Morsi's.

"Now you're dealing with a government [in Egypt] that has made Hamas one of its public enemies in terms of both rhetoric and in terms of the tightening of the tunnel trade – so obviously Egypt doesn't have Hamas's best interests at heart. But if it can get something out of its involvement, it will do so. If the main story coming out is that Egypt is intervening in the crisis, that will change the dominant story about Egypt in the international media – which is about human rights abuses."

A senior regional diplomat said that Egypt's involvement would ultimately be necessitated by the Egyptian public's sympathies for Gazans. "Even if the current Egyptian admin might not like Hamas, because the issue is so sensitive and so humanitarian they are not in a position to turn a blind eye to what's going on," said the diplomat. "That wouldn't go well with their own community."

With Hamas widely tarred in the Egyptian media since Morsi's ousting, reaction to the latest conflict in Gaza has nevertheless appeared more mixed than usual in Egypt. Local reporting suggests that there has not yet been any sizeable pro-Gaza rally in Cairo, while some Egyptian columnists have mulled over the difficulty of siding with either Hamas or Israel.

But the tide seemed to turn on Thursday, with Egypt's main state newspaper giving the issue greater prominence on its front page. The head of Cairo's al-Azhar mosque – the seat of Sunni learning worldwide, and an institution largely aligned with the Egyptian state – later issued a condemnation of Israel's actions.

Writing in one private Egyptian broadsheet, columnist and editor Emad Eddin Hussein said: "At the end of the day, Hamas is fighting with our first and last enemy: Israel … We are with Hamas as long as the enemy is Israel."