Annan said he was "extremely concerned about the dangerous situation in the occupied Palestinian Territory".
"The passage of foodstuffs and other essential supplies through the Karni commercial crossing should be ensured and restrictions on movement and access for UN agencies should be lifted forthwith," Annan said in a statement.
"I am appealing for urgent action to alleviate the desperate humanitarian situation of the civilian population."
Annan noted that Israeli airstrikes on Gaza's only power plant have impacted Gaza's hospitals, flour mills, water and sanitation systems, and called for the Israeli government to "act expeditiously" to replace the destroyed equipment.
"I reiterate my appeal to all concerned to exercise maximum restraint and to respect their obligations under international humanitarian law," said Annan, who is currently in Berlin.
UN humanitarian agencies, meanwhile, described severe power, water, food and sewage services in Gaza and called on both sides of the conflict to respect international humanitarian law regarding civilians.
In a separate joint statement, the UN agencies working in the occupied Palestinian territory said they were "alarmed by developments on the ground, which have seen innocent civilians, including children, killed, brought increased misery to hundreds of thousands of people and which will wreak far- reaching harm on Palestinian society."
"An already alarming situation in Gaza, with poverty rates at nearly 80 percent and unemployment at nearly 40 percent, is likely to deteriorate rapidly, unless immediate and urgent action is taken," they said.
The UN Relief and Works Agency (UNRWA) said Gaza was "on the brink of a public health disaster" since the Israeli airstrike on Gaza's only power plant on June 28.
With less than a fourth of the fuel needed to pump backup generators, the water utility's daily operation has been cut by two thirds, resulting in water shortages and a "critical" situation at the sewage plants, UNRWA said.
The World Health Organisation (WHO) said the current fuel supply would keep hospitals and health care centres running for a maximum of two weeks.
WHO estimated that 23 percent of the essential drug list will be out of stock within a month and expressed alarm about a tightening of restrictions on patients needing to leave Gaza for treatment.
The World Food Programme said it estimated in June 70 percent of the Gaza population already were unable to meet their daily food requirements without assistance.
The escalation of hostilities and the power shortages have aggravated food shortages, it said.
The Office of the High Commissioner for Human Rights said both sides in the conflict must respect international humanitarian rules.
"Whilst Israel has legitimate security concerns, international humanitarian law requires that the principles of proportionality and distinction between civilians and combatants be respected at all times," the commissioner said.
"The prohibition on targeting civilians is also being violated by Palestinian armed groups, launching missiles from the Gaza Strip into Israel, and must therefore end."
Israel has vowed to use everything in its power to increase the pressure on the embattled Hamas-led government to free 19-year-old Israeli Corporal Gilad Shalit and to stop rocket attacks.
Forty Palestinians and one Israeli soldier have been killed since Israel launched its massive military operation in Gaza late Wednesday.