The 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, which began its discussions to ease the embargo on Wednesday, noted that "existing security procedures to prevent the inflow of weapons and war material" would continue.
Ahmed al-Kord, from the Hamas-run Gaza government's ministry of social affairs, said that this statement by Israel was "just propaganda".
"It is the result of the international pressure against the Israelis about the siege," he said.
He said that only 130 of 4,000 items of basic supplies are allowed in.
"Our request is that the border should be open completely. This new Israeli system is not acceptable," he said.
Ismail Radwan, a senior Hamas leader, also dismissed the Israeli decision as an attempt to "relieve the pressure" following the flotilla incident.
"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.
Israel has faced mounting international callsto ease or lift the embargo following the killing by its commandos of nine pro-Palestinian Turkish activists during an attack on international waters of an aid convoy on May 31.
Israeli leaders say the troops acted in self-defence after the flotilla activists attacked them.
But preliminary autopsy reports revealed that the nine activists were shot a total of 30 times, some in the back of the head or in the back.
Israel imposed the blockade on the Gaza Strip soon after Hamas won a Palestinian legislative election in 2006.
Restrictions were tightened a year later after Hamas took control of the coastal Palestinian enclave after defeating its rival, Fatah, in a power struggle.
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.