Israel says it has authorised the entry to the Gaza Strip of 30 lorries carrying basic humanitarian supplies.
It was not immediately clear when the lorries would be allowed, however, as Palestinian militants have continued firing rockets and mortars overnight, reported BBC.
This follows a warning by UN relief officials that food in distribution centres would run out by Thursday.
Also on Thursday a delegation of senior European diplomats was barred access to by the Israeli authorities.
Israel stopped the transfer of goods - food and fuel included - for nearly a week, citing recent militant attacks. It has also prevented journalists, including from the BBC, from entering the territory.
Militants say the mortar and rocket fire is their response to what they say is Israeli aggression against Gaza.
The UN relief agency, Unrwa, distributes emergency aid to about half of Gaza's 1.5m population. Its spokeswoman Karen Konig Abu Zayd says the latest Israeli restrictions raise concerns about the future of humanitarian supplies to Gaza.
"This is the first time we've really been under such restrictions from the Israelis. They've always been good about letting us get in the basic humanitarian supplies of food and medicines, but now they're not even allowing us to do that," she told the BBC.
Israeli government spokesman Mark Regev says any improvement is dependent on the Hamas movement which runs the Gaza Strip:
"There's been a combat situation and it's very difficult to have unhindered functioning of the border crossings in a situation where shooting is going on," he said.
On Wednesday, Israeli troops killed four Palestinian militants from the Hamas movement, which has controlled Gaza since it wrested power from the Fatah-dominated Palestinian Authority in June 2007.
Witnesses said fighting broke out on the Gaza border after Israeli armoured vehicles crossed into the territory near Khan Younis.
The army said its soldiers were trying to stop militants plant a bomb near the security fence surrounding the strip.
Limited supplies of fuel were sent over on Tuesday after Gaza's only power plant ran out of diesel.
The plant provides most of the electricity used in Gaza City; Israel supplies most of the rest of the territory's energy needs, but the system is liable to become overloaded and blackouts are common.
Israel occupied Gaza in 1967, but pulled military forces and Jewish settlers out in the summer of 2005.
Access to the territory, which is home to about 1.5m Palestinians, remains under control of the Israel military, as does its airspace and territorial waters.
Egypt controls the southern entrance to Gaza at Rafah, and goes along with the policy of isolating the Hamas movement, which Israel and its allies brand a terrorist group.
Israel and Hamas agreed a truce in Gaza five months ago but fierce fighting resumed last week.