Friday's resolution won 142 votes in favour, six against with eight abstentions.
John Terrett, Al Jazeera's correspondent in New York, called the measure "a stinging rebuke for Israel".
"We now do have a General Assembly that has voted in favour of a resolution that doesn’t quite condemn Israel but does go a long way down the road towards it," our correspondent said
Security council resolution 1860 had also called for the "unimpeded provision and distribution throughout the Gaza Strip of humanitarian assistance, including of food, fuel and medical treatment".
Ryad Mansour, the Palestinian observer to the United Nations, welcomed the assembly's "almost unanimous vote" to pressure Israel to comply with resolution 1860.
"We shall prevail because of your support," he said.
Israel is demanding that rocket fire from Gaza ceases and that an international force is established to prevent weapons from being smuggled into Gaza.
Hamas wants Israeli troops to be withdrawn from the Gaza Strip immediately and for all crossings into the territory to be permanently re-opened. Israel has blockaded the Gaza Strip for more than 18 months, leaving the population of 1.5 million short of food, fuel and medical supplies.
While Israel says it reserves the right to use military action if under threat, its emergency security cabinet is expected to vote on Saturday in favour of a unilateral ceasefire in Gaza, according to the AFP news agency.
By Friday morning, 1,155 Palestinians had been killed and more than 5,200 injured since Israel launched its offensive on December 27. One-third of the dead are children.