Egypt's president, Mohamed Morsi, has said a ceasefire between Hamas and Israel was imminent, following a week of violence in Gaza, and a cessation of hostilities could be near.

In public remarks made at the funeral of his sister in the Nile delta town of Zagazig, Morsi was quoted by a spokesman as saying that the "Israeli aggression" would end "today, Tuesday".

His comments come ahead of a visit by Hillary Clinton to the region, who will visit Jerusalem, Ramallah on the West Bank and Cairo to discuss a long-term ceasefire.

Morsi, a member of the Muslim Brotherhood, has been at the forefront of efforts to secure a truce and appeared to confirm growing speculation that an end to the latest bout of violence was close. "The efforts to conclude a truce between the Palestinian and Israeli sides will produce positive results in the next few hours," he was quoted as saying. "Egypt has been trying to mediate a truce to end the conflict."

A day earlier, Morsi had spoken to Barack Obama by phone, who has insisted that Hamas stop firing rockets into Israel, while "regretting" the civilian Palestinian deaths in the Israeli operation.

Although both sides have made public demands of their preconditions for a ceasefire, sources suggested that in the private negotiations in Cairo and elsewhere in recent days both Hamas and Israel were close to agreeing an end to hostilities.

Morsi's remarks came despite a bellicose speech by Mohamed Deif, the head of Hamas's military wing, saying that his men were preparing for a ground war. Sources suggest, however, that despite more rockets fired from Gaza and continuing Israeli strikes, progress has been made in talks.

The arrival of Clinton has raised hopes of an end to the violence. An Israeli source said she was expected to meet the Israeli prime minister, Binyamin Netanyahu, on Wednesday.

A US state department official said: "Her visits will build on American engagement with regional leaders over the past days – including intensive engagement by President Obama with prime minister Netanyahu and President Morsi – to support de-escalation of violence and a durable outcome that ends the rocket attacks on Israeli cities and towns and restores a broader calm."

One of the stumbling blocks is understood to be the insistence by Hamas that Israel end assassinations of its members and lift the long-lasting economic blockade of Gaza. It was suggested on Monday that this issue may be left for a future negotiation on a long-term ceasefire after a halt to the violence had been achieved.

A western official, speaking a little before Morsi's comments, told the Guardian there was optimism that a ceasefire might be in place soon. Senior western leaders and officials, including Obama and the British foreign secretary, William Hague, have been calling for a "de-escalation" for several days, which led to Israel putting on hold plans for a ground offensive against the coastal enclave. According to reports from Israel, it had given until Thursday to conclude a ceasefire.

Some 115 Palestinians have died in a week of fighting, the majority of them civilians, including 27 children, hospital officials said. Three Israelis died last week when a rocket from Gaza struck their house.

In Cairo, the UN secretary general, Ban Ki-moon, called for an immediate ceasefire and said an Israeli invasion of Gaza would be a "dangerous escalation" that had to be avoided. He had held talks in Cairo with the Arab League chief, Nabil Elaraby, and the Egyptian prime minister, Hisham Kandil, before travelling to Israel for discussions with Netanyahu. Ban planned to return to Egypt on Wednesday to see Morsi, who was unavailable on Tuesday, due to the death of his sister.

Israel's leaders weighed the benefits and risks of sending tanks and infantry into Gaza two months before an Israeli election, and indicated they would prefer a diplomatic path backed by world powers, including the US, the European Union and Russia.