Rise in taxes imposed by Hamas on various products sparks controversy in the strip.
“Israel seeks to keep out of Gaza weapons and material that Hamas uses to prepare and carry out terror and rocket attacks towards Israel and its civilians,” the statement said.
“All other goods will be allowed into Gaza.”
Israel also said that it will consider additional ways of allowing more Palestinians to leave the Gaza Strip for medical and humanitarian reasons.
The Israeli move follows global criticism of the blockade in the wake of Israel’s deadly raid on a flotilla of Gaza-bound aid ships last month, that left nine people dead.
Hamas said Israel’s previous announcement about easing the blockade was “propaganda”
According to Sunday’s announcement, Israel would allow desperately needed construction materials for projects approved by the Palestinian Authority, and as long as they are under international supervision.
The statement from Netanyahu’s office said that goods would be let in for projects including schools, health facilities, water treatment and sanitation.
Up to now, Israel has banned most construction materials, including cement.
The UN has complained that the ban on construction materials is preventing reconstruction of the territory which was devastated by an Israeli offensive in late 2008 and early 2009.
Washington reacted positively to Israel’s announcement.
“We believe that the implementation of the policy announced by the government of Israel today should improve life for the people of Gaza, and we will continue to support that effort going forward,” Robert Gibbs, the White House press secretary, said in a statement.
It also said that Barack Obama, the US president, would discuss “additional steps” with Netanyahu during a visit to Washington by the latter on July 6.
Several organisations, including Amnesty International, have recently called on the Israeli government to lift the blockade entirely. The International Commitee of the Red Cross last week called it a violation of the Fourth Geneva Convention.
Al Jazeera’s Ayman Mohyeldin, in Jerusalem, said: “There is no doubt that a great deal of the attention that has focused on changing or adjusting Israel’s policy on Gaza has been in the wake of the ‘Freedom Flotilla’ incident back on May 31.”
He also said that in Israel there was “strong criticism” that the government has caved under international pressure with the decision and consequently jeopardised the country’s security.
However, he added that other people in Israel are saying that the move is simply an attempt to deflect or alleviate some of the pressure and Israel should end the blockade totally.
Mohyeldin added that the move had been facilitated by Tony Blair, the international Middle East envoy, who held talks with Netanyahu during the past few days.
Hamas, which seized control of the Gaza Strip from Fatah in 2007, did not immediately react to the annoncement.
About 1.5 million Palestinians live in the Gaza Strip and the vast majority depend on aid from the UN and international organisations to survive.
The embargo is in place to weaken Hamas and has reduced the amount of imports into the Gaza Strip to about one quarter of the volume received at the end of 2005.