Hamas' armed wing, critical of what it calls Washington's political and financial support for Israel, has called on Muslims to attack US targets, urging them to teach the American enemy harsh lessons.
The dead included 13 members of one family.
Israeli leaders have voiced remorse for the killings saying they were probably caused by shells which overshot after being aimed at Palestinian militants.
The shelling hit homes in the town of Beit Hanun, just a day after Israel ended a week-long ground offensive targeting militants in the area.
The deadliest military strike in four years has prompted the Jewish state to declare a high alert and rallied Palestinians after months of factional infighting.
Palestinian medics say eight children and five women were among those killed, with 11 from the same family.
Dozens were also wounded when shells slammed into a row of five apartment blocks in the early morning.
"I ran away and saw a second shell strike the houses. A shell fell on people who had run out into the street," said resident Ataf Ahmed.
Another two Palestinians, including a Hamas gunman, were killed in the nearby refugee camp of Jabaliya. Five others, including four militants, were killed in a pre-dawn raid near the flashpoint city of Jenin in the occupied West Bank, medics said.
Israel apologises
Defence Minister Amir Peretz ordered a halt to all artillery fire in the coastal strip pending an inquiry.
But officials say the four-month operation against militants -- launched after the seizure of Corporal Gilad Shalit -- would continue, with an air raid later killing two militants in eastern Gaza City.
In a joint statement, Prime Minister Ehud Olmert and Mr Peretz "expressed their regret over the deaths of Palestinian civilians" and "offered... urgent humanitarian assistance and immediate medical care for the wounded."
"Israel does everything to avoid hitting innocent civilian populations during operations, unfortunately tragedies sometimes happen. We are sorry," Foreign Minister Tzipi Livni said.
An army spokeswoman said artillery had been trained on an area used by Palestinian militants to fire rockets into Israel. Twelve rockets hit Israel over the past 24 hours and some 50 over the past week, she said.
Palestinians vow revenge
The deaths prompted moderate Palestinian president Mahmud Abbas to accuse Israel of destroying peace hopes and rival Palestinian factions Hamas and Fatah to call for renewed suicide attacks.
Israeli police went on alert following the threats.
Mr Abbas condemned Israel's "terrible massacre" and together with Hamas Prime Minister Ismail Haniya demanded an urgent UN Security Council meeting to stop the bloodshed.
"You (the Israelis) do not want peace at all. You have destroyed all chances of peace and you should bear all the responsibility," he said.
International outrage
While Israeli leaders offered regret about the "tragedy" and offered aid for the wounded, the international community urged a halt to Gaza operations, which have killed more than 300 Palestinians since Corporal Shalit's capture in late June.
US Secretary of State Condoleezza Rice called Mr Abbas to express "deep sorrow" over the deaths, said his spokesman Nabil Abu Rudeina.
The deaths came just five days before the Israeli Prime Minister was due to meet US President George W Bush in Washington, and Mr Abbas asked Ms Rice "to move to stop Israeli aggression in the Palestinian territories," Mr Rudeina said.
But US State Department spokesman Sean McCormack said "the response to the loss of innocent lives is not go out and take revenge ... on other innocents."
The UN special envoy for the Middle East, Alvaro de Soto, urged Israel and the Palestinians to stop attacks against each other.
The European Union called the event "profoundly shocking," saying "Israel has a right to defend itself, but not at the price of the lives of the innocent."