A Gaza City house has been shelled and other areas in Gaza have been fired upon since an Israeli-declared seven-hour humanitarian truce has come into effect.
The Gaza Health Ministry said a child was killed and 30 people, mostly women and children, were wounded in the strike on Monday on a house in Shati refugee camp.
An Israeli military spokeswoman told news agency Reuters she was checking the report.
Israel earlier declared that it was holding fire in parts of the Gaza Strip for seven hours, amid world outrage over a deadly strike on a UN school in the Palestinian territory.
Monday's limited and unilateral truce, between 0700-1400 GMT, was announced after world powers fiercely condemned the previous day's attack that left 10 Palestinians sheltering at a school dead, as Israel was pulling some of its troops from Gaza.
The Israeli army said the "humanitarian window" would take place in all of the Gaza Strip except the area east of the southern city of Rafah, "where clashes were still ongoing and there was an Israeli military presence".
The army warned in a statement that it would "respond to any attempt to exploit this window" and attack civilians and soldiers during the truce.
It also said that residents of Abasan al Kabira and Abasan al Saghira, two villages east of Khan Younis in southern Gaza, could return home.
Al Jazeera's Nicole Johnston, reporting from the rural area of Khuzaa, said temporary ceasefires imposed since Israel's offensive began had not been successful, even when sponsored by the UN.
"Israel has made it clear areas where the army is continuing its operations will be exempt, and that includes areas of Rafah. We know that in certain places like Beit Lahiya, Israel has come out and told people they can go home but people have been too frightened to do so," she said.
"This is a very shaky ceasefire indeed," Johnston said, as tank shelling could be heard in the background.
The Israeli announcement was received with distrust by the Palestinian group Hamas, whose spokesman in Gaza, Sami Abu Zuhri, warned the local population to be wary.
"Israel’s so-called humanitarian ceasefire is unilateral and it comes in a time when the Zionist enemy wants to distract the world from the massacres they have committed against our people in Gaza," Abu Zuhri told Hamas's Al Aqsa television station.
"We don’t trust their intentions and we ask our people to take extreme caution."
Al Jazeera's James Bays, reporting from West Jerusalem, described the ceasefire as "a conditional, partial pause" and said there were possible military advantages for the Israelis in having a break from the bombardment.
"There is such as thing as battle damage assessment. You can get your aircraft and your drones up and look at what's been hit and what's not been hit. I'm sure it's proving useful to the military planners," Bays said.
The Israeli army said that it had on Sunday targeted three Islamic Jihad fighters on a motorbike "in vicinity of an UNRWA school in Rafah".
Mark Regev, Israel's government spokesman, told Al Jazeera the area hit adjacent to the school was "a legitimate terrorist target".
"I said there was a specific target - three operatives from Islamic Jihad. We know there appears to be collateral damage but we don't yet know how it was caused. Was it our ordnance or was it ordnance carried by the operatives we targeted?" he said.
"Hamas and other terrorists repeatedly shoot at Israel from adjacent to UN facilities. We are doing our best in a very complicated combat situation to hit the terrorists and not to target civilians."
Ban Ki-moon, UN secretary-general, called the attack near the school sheltering some 3,000 Palestinians who had fled their homes due to the fighting "a moral outrage and a criminal act".
"This madness must stop," he said.
Jen Psaki, the State Department spokesperson, said the US was "appalled" by the attack and called for a "full and prompt" investigation.
"Israel must do more to meet its own standards and avoid civilian casualties," she said.
French President Francois Hollande said the bombing near the school was "unacceptable", backing calls by Ban "to ask that those responsible for this violation of international law answer for their actions", without saying who he considered responsible.
In a statement early on Monday, Benjamin Netanyahu, Israeli prime minister, said "Israel does not aim its fire at civilians and is sorry for any attack that unintentionally hits civilians", without directly addressing the Rafah attack.
Israeli attacks on Gaza continued on Monday and killed 11 people raising the death toll since the July 8 beginning of the confrontation to at least 1,817, according to Palestinian medical sources.
An Israeli air raid killed an Islamic Jihad commander in the Gaza Strip just hours before Monday's partial truce went into effect.
The Islamic Jihad group - a close ally of Hamas - said Daniel Mansour, its commander in the northern part of Gaza, died when an Israeli strike hit his home just before dawn.