The announcement of an impending ceasefire was made overnight between Thursday and Friday and included that Israeli troops will remain in the Gaza Strip over the 72 hours of calm.
An envoy representing the Palestinians is expected to head for Cairo to meet an Israeli delegation dispatched Wednesday, for talks on a more stable truce to last beyond the 72 hours and bring the fighting to an end..
"We urge all parties to act with restraint until this humanitarian ceasefire begins, and to fully abide by their commitments during the ceasefire," Kerry and Ban said upon announcing the agreement. "This ceasefire is critical to giving innocent civilians a much-needed reprieve from violence."
The statement was released in New Delhi, where Secretary of State John Kerry is now meeting with Indian officials.
Quartet Representative Tony Blair expressed relief at the news of a ceasefire saying that "Too many innocent lives have been lost in Gaza, and lives left in ruins. In order to give some hope back to the people of Gaza, its people have to see an end to the terrible loss of life, the destruction and the isolation from the world."
He also addressed Israeli security concerns saying, "Israelis need to know that they have genuine protection from rockets, tunnels and terror attacks. There must be a new and hopeful future for both sides."
Blair did stress however, that the international community must take advantage of this window of calm to forge a permanent agreement. "This gives the sides, through the Egyptian mediators, the opportunity to reach a sustainable arrangement that will address Israel's security concerns, as well as ensure a better future for Gazans."
British Foreign Secretary Philip Hammond gave positive feedback to the ceasefire initiative saying, "I welcome the news of an agreement of a ceasefire to halt the violence we have seen. This is an achievement we have all been working tirelessly for, with visits around the region and talks in Paris last weekend."
He then called for concrete action to reach a more stable truce between Israelis and Palestinians. "We should now redouble our efforts and leave no stone unturned, to ensure this is a lasting and durable ceasefire to make way for substantial discussions to resolve the underlying issues on both sides."
Australia's Prime Minister Tony Abbott also weighed in, welcoming a ceasefire between Israel and Hamas as "a marvelous humanitarian thing."
He said on Friday that Australia had been working at the United Nations and elsewhere for an immediate ceasefire.
Abbott told reporters he deplores "the indiscriminate rain of missiles from Gaza on to Israel" and "any actions which result in civilian deaths."
After an Israeli delegation arrived in Cairo on Wednesday to advance talks for a ceasefire in Gaza, the Palestinian delegation was expected to arrive in Egypt on Thursday night, Al-Manar reported.
The Palestinian delegation includes yet unnamed representatives from both Hamas and Islamic Jihad, and was set to be headed by Palestinian Authority President Mahmoud Abbas.
The Israeli delegation includes Shin Bet chief Yoram Cohen and the head of the Policy and Political-Military Affairs department in the Defense Ministry Maj.-Gen. (Res.) Amos Gilad.
PLO official Wasel Abu-Youssef told Asharq Al-Awsat that there are "talks between Palestinian officials of the highest ranks in order to establish a three- or a five-days ceasefire, following which negotiations will be held in Cairo to reach a permanent agreement."
He said the Palestinian leadership was working alongside the UN, Qatar, Turkey, the US, Russia and others to reach a long-term truce.
Other Palestinian officials said Qatar intends to join forces with Egypt to help reach an agreement.
Reuters contributed to this report.