The deadly shelling, in which eight children and five women were among those killed, came just five days before Prime Minister Ehud Olmert holds a second summit with US President George W. Bush at the White House.
Israel's leadership rapidly expressed regret over the incident, while Olmert and Defence Minister Amir Peretz offered humanitarian assistance to the wounded in the northern town of Beit Hanun after shells slammed into private homes.
"The two men offered the Palestinian Authority urgent humanitarian assistance and immediate medical care for the wounded," the prime minister's office announced after urgent talks between Olmert and Peretz.
Peretz told the premier he had ordered "an urgent investigation" and a "halt to artillery fire" in Gaza until "the inquiry into the circumstances, the background and the considerations that led to the tragic results" was over.
Peretz ordered that Gaza's Rafah crossing with Egypt be reopened for 24 hours so wounded could be taken to hospitals in Egypt, and he will examine whether that should be extended, the defence ministry said.
The Rafah crossing, Gaza's sole border crossing that bypasses Israel, has been closed nearly continuously since late June, after Gaza-based militants seized a soldier and killed two others in a cross-border raid.
An army spokeswoman said Israeli artillery had targeted an area from which 'militants' fired rockets.
Army radio reported that the investigation would determine why the shells exploded in Beit Hanun, several hundred metres (yards) away from the intended target.
While Foreign Minister Tzipi Livni joined the ranks of leaders expressing regret, a senior official vowed that operations against Palestinian militants inside Gaza -- already into a fifth month -- would continue.
"Israel does everything to avoid hitting innocent civilian populations during operations, unfortunately tragedies sometimes happen. We are sorry," said Livni.
"Israel last year evacuated the Gaza Strip to provide an opportunity to establish new relations with the Palestinians.
"Unfortunately, since the withdrawal, towns in southern Israel have become a target for fire from Palestinian terrorists," she added.
An official in the prime minister's office told AFP Israel would continue operations against militant groups in the Gaza Strip.
"What happened in Beit Hanun was a tragedy, but the Israeli army will continue its operations against rocket fire, weapons smuggling and to release Gilad Shalit," the official said.
Israel has been operating inside the Gaza Strip since late June in raids that have left more than 300 Palestinians dead.
A report by the Physicians for Human Rights group released on Wednesday said that more than 60 percent of those killed have been civilians and more than 20 percent have been children.
Deputy Defence Minister Ephraim Sneh levelled the same warning that the offensive will go on.
"The fighting will continue as long as fire against the Israeli civilian population continues and as long as the terrorist organisations strengthen themselves thanks to arms trafficking from Egypt," he said.
"We will continue to take measures to weaken the political and economic base of Hamas in the Gaza Strip," Sneh added.
On the diplomatic front, officials sought to minimise the potential fallout of the deaths at a time when contact between Israel and the Palestinians has been frozen since the Hamas movement took office last March.
"There is no reason for the Beit Hanun tragedy to influence in any way the meeting between the prime minister and President Bush," Olmert's spokeswoman Miri Eisin said.
The United States, Israel's chief ally, said last week, but well before the latest deaths, that Israeli operations in Gaza were an issue of "self-defence".

Copyright AFP (Agence France-Presse), 2006