Israeli officials said at least 12 rockets were fired by Palestinian militants into southern Israel.
Two Norwegian doctors, who have been working in the Gaza Strip, say the main hospital is close to collapse, and that patients are dying because of a lack of specialist doctors and basic medical equipment.
Doctors Mads Gilbert and Erik Fosse said half of their patients were civilians, some of them young children with shrapnel and blast wounds.
They also said 12 ambulance staff had been killed in shelling, despite their clearly-marked vehicles.
As Israel's cabinet met in Jerusalem to consider its next move, Prime Minister Olmert said: "This is a time to translate our achievements into the goals we have set."
He praised the military's "impressive gains " in Gaza, adding: "Israel is nearing the goals which it set itself, but more patience, determination and effort is still demanded."
Referring to last week's UN Security Council call for an immediate ceasefire, Mr Olmert said "nobody should be allowed to decide for us if we are allowed to strike". Both Hamas and Israel have rejected the UN resolution.
In Cairo, Egypt's state news agency reported progress in talks between Egypt and Hamas, without providing details.
Talks between Hamas and Egyptian intelligence chief Omar Suleiman were described by an unnamed intelligence official as "positive".
Former UK Prime Minister Tony Blair, now Middle East envoy for the Quartet - the US, EU, UN and Russia - is due to meet Egyptian President Hosni Mubarak in Cairo on Monday morning.
Confirmation that reservists have been deployed in Gaza came a day after Israel dropped leaflets and left phone messages warning Gazans to stay away from areas used by Hamas, saying that its operation would soon enter "phase three".
Late on Sunday, an Israeli army spokesman said: "More and more [reserve soldiers] have been incorporated into the operations. This is not to suggest that there is a big new push."
The Israeli army meanwhile denied deploying white phosphorus bombs in Gaza, after Palestinian medics said they had treated patients for burns caused by the munition.
Army spokesman Capt Guy Spigelman told the BBC that Israel "categorically denied" using white phosphorus in Gaza, saying other "smoke bombs and flares" were being deployed.
Israel began Operation Cast Lead as a six-month truce between it and Hamas unravelled. It comes weeks before a parliamentary election in Israel.
Israel hopes the scale of its operation will greatly reduce the number of missiles fired from Gaza onto Israeli towns, and also erode support for Hamas.
The Islamist movement won elections in Palestinian territories in 2006 before seizing control of Gaza a year later, ousting its secular Palestinian rival Fatah, which now holds sway in parts of the West Bank.
On Sunday militants fired a barrage of rockets from Gaza, two of which struck 42km (26 miles) inside southern Israel at the city of Beersheba, causing damage but no casualties.
In clashes in Gaza City, at least 10 Palestinians died in a gun battle involving Israeli forces, while at least five Palestinian civilians were killed by Israeli tank fire further north at Beit Lahiya, said medical officials.
The home of Ahmed Jabari, the head of Hamas's military wing, was destroyed in an air strike at Shujaia, a suburb of densely-populated Gaza City, according to the Israeli military.
Israel is preventing international journalists from entering the coastal strip, and none of the incidents can be independently confirmed.
Israel said its warplanes had also bombed sites on the Egypt-Gaza frontier near the town of Rafah, including a mosque allegedly used as a weapons storage depot and militant training camp.
Two Egyptian policemen were injured on Sunday by shrapnel flying through the fence from Israeli rockets landing on the Gaza side of the Rafah border crossing.
Its ground forces were involved in a "number of incidents" as they pushed into the south of Gaza City and reached a key junction to its north, the Israeli military said.
Reports quoted Hamas and the smaller militant group Islamic Jihad as saying they had ambushed the Israelis, engaging them in heavy fighting.
Many Gaza City civilians have reportedly fled their homes. Aid agencies say Gaza's 1.5 million residents are in urgent need of food and medical aid.
On Sunday pro-Palestine demonstrations continued across Europe and the Middle East.
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