In a telephone call to Olmert, Ban Ki-moon, the UN secretary-general,"expressed disappointment that the violence is continuing on the ground in disregard" of the Security Council resolution.
The Israeli army said that 30 rockets were fired into southern Israel on Friday morning, injuring one person. Four rockets hit Beersheba, a town about 40km from the Israeli-Gaza border.
More than 50 air raids were reported to have hit across the Gaza Strip on Friday as the death passed 800 Palestinians over the 14 days of the Israeli assault.
More than 250 Palestinian children and nearly 60 women are among the dead, according to the UN.
Among the buildings hit was an eight-storey building in Gaza City housing the offices of a number of news outlets.
Tanks also shelled targets in Jabaliya and Beit Lahiya in the north and in the Zeitun neighbourhood of Gaza City, witnesses said.
"In the outskirts of the eastern Jabaliya area there have been Israeli ground forces operating and they have been clashing quite intensely with Palestinian fighters," Al Jazeera's Sherine Tadros, reporting from Gaza City, said.
"Those calls for a ceasefire from the United Nations are obviously not manifesting themselves on the ground here."
Raafat Morra, a Hamas official in Beirut, said the Palestinian group also rejected the UN resolution, as "it is not in the best interest of the Palestinian people".
A senior delegation from Hamas was travelling to Cairo for talks expected on Saturday on an alternative ceasefire plan that calls for an immediate halt to violence and subsequent talks on securing Gaza's border and reopening the border crossings.
Marwan Bishara, Al Jazeera's senior political analyst, said: "The failure of the UN security council resolution to institute a ceasefire on the ground is throwing the ball back in the Egyptian court.
"I think there will be intensifed efforts. Unfortunately the gap between Hamas and Israel is too big and Hamas would not accept any serious efforts at calming the situation as long as Israeli tanks are in the populated areas of the Gaza Strip."
The UN resolution, which was backed by 14 nations on the 15-member body, with only the US abstaining, called for an "immediate, durable and fully respected" ceasefire.
It also said border crossings into Gaza should be re-opened and measures put in place to prevent the smuggling of weapons into the Gaza Strip.
The resolution underlined there should be "unimpeded provision" and distribution of aid into the territory, where Gazans have been starved of fuel, food and medical supplies for months following Israel’s crippling blockade.
Mark Regev, an Israeli government spokesman, told Al Jazeera the military operation would continue to target "the Hamas military apparatus".
"We want Hamas leaders to understand that when they shoot rockets into Israel trying to kill our civilians that is counterproductive to their most basic interests," he said.
Regev said that Israel had not rejected the UN resolution and wanted to see "a sustained, durable ceasefire in the south".
"Does anyone really expect that when Hamas says 'this does not concern us' and continues to shoot at Israel we will just hold our hands behind our backs and say 'yes, please, target our citizens and try to kill our people, we'll do nothing," he said.
Thirteen Israelis have been killed since the beginning of the offensive, three by continued Palestinian rocket fire into Israel.
Aid to resume
Meanwhile, UN aid workers were set to resume humanitarian activities, suspended after a UN convoy came under fire from Israeli forces.
|Israeli artillery shells hit targets in
Jabalia and Beit Lahiya [AFP]
"The UN received credible assurances [from Israel] that the security of UN personnel, installations and humanitarian operations would be fully respected," Michele Montas, a UN spokeswoman, said.
On Thursday, a contract worker was killed when a Unwra aid convoy came under Israeli fire during a three-hour armistice agreed by the Israelis in order to deliver essential supplies to Gaza residents.
"The need on the ground is dire," Nancy Ronan, a spokeswoman for the UN's World Food Programme, told the AFP news agency at Egypt's Rafah border crossing earlier.
"We got food into Gaza, but we now have a problem distributing it because of the security situation."
The UN also said on Friday that 30 Palestinians were killed in Gaza on January 4 after the Israeli army moved dozens of civilians to a building which troops later shelled.
A special report by the UN's Office for the Co-ordinator of Humanitarian Affairs (OCHA) said 110 Gazans were transferred to the house and that the Israeli army were investigating the incident.