The United Nations has called for an immediate and unconditional ceasefire in Gaza as fighting between Hamas and Israel subsided overnight following a series of ceasefire announcements by both sides, each of which was rejected by the other amid mutual blame and recrimination.

The UN security council issued a presidential statement just after midnight in New York, as the Muslim holiday of Eid al-Fitr, which marks the end of the holy month of Ramadan, was beginning. The move will increase pressure on Israel and Hamas to agree a long-term truce to end the conflict, now in its 21st day.

The statement called on the parties to the conflict "to accept and fully implement the humanitarian ceasefire into the Eid period and beyond” and "to engage in efforts to achieve a durable and fully respected ceasefire, based on the Egyptian initiative”.

It noted "grave concern regarding the deterioration in the situation as a result of the crisis related to Gaza and the loss of civilian lives and casualties” and called for Israel and Hamas to respect international law.

US president Barack Obama, in a phone call on Sunday to Israel's prime minister, Binyamin Netanyahu, stated his concern at the rising number of civilian deaths and urged an immediate, unconditional ceasefire.

Saying the US backed a ceasefire plan tabled two weeks ago by Egypt, Obama stressed the importance of "ensuring Israel’s security, protecting civilians, alleviating Gaza’s humanitarian crisis and enacting a sustainable ceasefire that both allows Palestinians in Gaza to lead normal lives and addresses Gaza’s long-term development and economic needs, while strengthening the Palestinian Authority".

But amid a confusing sequence of unilateral temporary ceasefires, there was little sign of a longer-term deal to end the military confrontation, which has claimed about 1,100 lives, the vast majority of them Palestinian civilians. The US secretary of state, John Kerry, returned to Washington at the weekend after his efforts to forge a ceasefire agreement between the two sides failed.

On Monday, Haaretz reported that the Israel Defence Forces had ceased striking targets within the Gaza Strip. It quoted a senior officer as saying "the situation now is being called a ceasefire with no restrictions. The central effort is the tunnels. We need a few more days [to take care of the tunnels]n… But we are also considering other possibilities, in the operative sense as well – in case we are called to keep fighting and progressing."

In the hours following a Hamas call for a 24-hour humanitarian ceasefire from 2pm on Sunday to mark the start of Eid, rockets were launched from Gaza and Israel carried out air strikes. Even so, in Gaza City people ventured out to stock up on food and essentials for the three-day holiday.

"In response to UN intervention and considering the situation of our people and the occasion of Eid, it has been agreed among resistance factions to endorse a 24-hour humanitarian calm, starting from 2pm on Sunday," Sami Abu Zuhri, a Hamas spokesman, told Reuters.

Israel, however, rejected the call, and Netanyahu later said the militants had "violated even their own ceasefire".

"They are shooting at us as we speak," he said in a series of interviews on US television networks, adding: "Under these circumstances, Israel will do what it must do to defend its people."

Khaled Mishal, Hamas's leader in exile, told PBS that Israel must end its occupation. "We are not fanatics. We are not fundamentalists. We are not actually fighting the Jews because they are Jews per se. We do not fight any other races. We fight the occupiers," he said.

There was a 12-hour lull in Israeli military action on Saturday in response to a UN call. Hamas did not formally sign up to the ceasefire, but refrained from rocket fire for its duration. Israel later extended the ceasefire by four hours to midnight on Saturday, then said it would withhold fire for a further 24 hours until midnight on Sunday. It resumed attacks on Sunday morning, however, in response to rocket fire from Gaza. Hamas's unilateral ceasefire announcement came shortly afterwards.