Al Jazeera's Ayman Mohyeldin, reporting from Jerusalem, said the statement made no reference to the naval blockade that Israel also imposes on Gaza.
"Looking at the statement in its entirety, the international community cannot be pleased with this, as they have been asking for a lifting of the blockade," he said.
Thursday's announcement appeared to indicate that Israel would allow international organisations, such as the UN, to import previously banned building materials, vital to reconstruction after its war on Gaza.
The security cabinet, however, noted that "existing security procedures to prevent the inflow of weapons and war material" would continue.
While an exact list of the products that will be allowed into Gaza has not been released, the Ha'aretz newspaper reported the Israeli-approved items could include all food items, toys, stationery, kitchen utensils and mattresses .
"The detail is what matters," Catherine Ashton, the European Union's foreign policy chief, said in response to the Israeli decision.
Israel must "make sure that many, many more goods can get in to Gaza to enable people to reconstruct their homes, to build schools, to place infrastructure, and also to enable people to get on with ordinary lives," Ashton said.
Malcolm Smart, Amnesty International's director for the Middle East and North Africa, said Israel's announcement was not enough.
"Israel must now comply with its obligations as the occupying power under international law and immediately lift the blockade," Smart said.
"Just as important as allowing goods into Gaza is allowing exports to leave Gaza, yet there is no mention of this in today's announcement.
"Banning the vast majority of exports, raw materials and the movement of people has destroyed the economy of Gaza, and pushed its population into unemployment, poverty and dependency on aid agencies for survival. These problems will not be solved while the blockade continues."
The blockade was imposed in 2007 after Hamas took control of the territory.
Ismail Radwan, a senior Hamas leader, also dismissed the Israeli decision as an attempt to "relieve the pressure" following the attack on the aid flotilla on May 31.
Israel has faced mounting international callsto ease or lift the blockade after its soldiers attacked a Gaza-bound aid ship and killed nine pro-Palestinian activists in international waters.
"We in Hamas reject the Zionist decision, which is an attempt to obscure the international decision to completely lift the siege on the Gaza Strip," Radwan said.
In the West Bank, the Palestinian Authority which rivals Hamas, also called for a complete end to the Gaza blockade.
"The siege is collective punishment and it must be lifted," Saeb Erekat, a spokesperson for the Palestinain Authority led by Mahmoud Abbas, the president, said.
Israel says the blockade is necessary to prevent arms smuggling to Hamas.
But the International Committee of the Red Cross has described it as illegal.