Aid was allowed in to Gaza on Monday but Israel then shut the crossings
The UN's top human rights official has said Israel's blockade of Gaza deprives Palestinians of the "most basic human rights" and should end immediately.
High Commissioner Navi Pillay called for "dignity and basic welfare" to be restored to the 1.5m people affected by the blockade for months.
Her comments came as the Israeli troops entered the southern Gaza Strip, clashing with Palestinian gunmen there.
Crossings into Gaza Strip were closed again by Israeli defence officials.
Israel described the incursion, close to the southern town of Rafah, as a "routine operation".
Ms Pillay issued a statement from UN offices in Geneva criticising the blockade: "This is in direct contravention of international human rights and humanitarian law. It must end now."
A convoy of 33 trucks of humanitarian aid was allowed in on Monday, but United Nations officials say the supplies will run out within days.
Israel says it has tightened its blockade of Gaza in response to recent rocket attacks by Palestinian militants, which have caused minor damage but no casualties.
Ms Pillay called on Israel to let aid, including food, medical supplies and fuel, into Gaza.
She also said electricity, water and other essential services should be restored immediately, and restrictions lifted on the movement of civilians for medical, educational and religious purposes.
"Decisive steps must be taken to preserve the dignity and basic welfare of the civilian population, more than half of whom are children," she added.
Describing the situation as "massive humanitarian suffering", Ms Pillay said Israel had a duty under international law to ensure food and medical supplies are distributed.
During Tuesday's incursion, witnesses said the Israeli troops were accompanied by bulldozers which destroyed agricultural land east of the town of Rafah, in southern Gaza.
There was no immediate reports of any injuries or deaths.
The Israeli military described the incursion as "a routine operation to uncover explosive devices near the border fence in the southern Gaza Strip", the Associated Press news agency reported.
It said two mortars were fired at troops, causing no injuries or damage.
With the crossings shut, a coalition of aid agencies which had been due to hold a meeting in Gaza instead held the event in the car park at Erez, the main crossing for people into Gaza, in protest at being denied entry to the Strip.
They called on the Israeli government to allow them "unimpeded humanitarian access" to help Gaza's residents.
At least 16 Palestinian militants have been killed in skirmishes with Israeli forces along the border in the past two weeks.
Israel and the Palestinian Hamas group agreed a ceasefire last July, but it has been under serious strain since early in November.