GENEVA, Sept 10 (Reuters) - United Nations Secretary General Ban Ki-moon warned Israel on Monday that keeping its long-standing blockade of Gaza would only condemn the area's people to lasting poverty and play into the hands of extremists in the Middle East.

In a speech to the world body's Human Rights Council, Ban also blamed what he called "indiscriminate rocket fire" into Israel from Hamas-controlled Gaza and serious rights violations there for "the immense human suffering" of its population.

"I urge Israel to lift its harsh restrictions in order to ease the plight of civilians and bring an end to the closure," the U.N. chief declared in a reference to the blockade which the Israel government argues is a security measure.

"Keeping a large and dense population in unremitting poverty is in nobody's interest except that of the most extreme radicals in the region," he declared.

Israel says its land-and-sea blockade is part of an effort to prevent weaponry and other equipment that could help build an offensive military potential reaching the territory's Hamas Islamist rulers and other militant groups based there.

Ban, whose comments were echoed at the 47-nation council by the U.N.'s High Commissioner for Human Rights Navi Pillay, also urged Israel to respect Palestinian rights and international law and support efforts to build a stable Palestinian state.

A lasting solution to the Middle East conflict required a negotiated agreement ending the 45-year-long occupation and creating "an independent, sovereign, democratic and viable Palestinian state" at peace with Israel, he said.

Peace negotiations between Israel and the Palestinian Authority in the West Bank have long been stalled with both sides blaming the other. The Palestinians say Israeli settlement activity is a main barrier to meaningful negotiations.

That point was raised by Pillay, a former judge in the International Criminal Court, in her address to the council. She pointed to settlement expansion "as well as violence by Israeli settlers against Palestinians" as a source of tension.

She also called on Israel to free Palestinians, totalling around 4,000, held without trial.

But she also criticised the rocket fire from Gaza and "arbitrary detention and ill-treatment" of people held by Palestinian security forces in Gaza and the West Bank.

Hamas says Palestinian factions are committed to self-restraint, arguing that rockets are used in self-defence and are fired individually and not as part of a systematic assault on Israeli villages and towns across the border.

Justice Minister Ali Mhana of the Palestinian Authority, which has held sway only in the West Bank since Hamas took control of Gaza in 2007, welcomed constructive criticism of any "shortcoming in our performance in the field of human rights."

It was working hard to prevent abuses, he said, speaking in Ramallah.