UNITED NATIONS  The United Nations secretary general, Ban Ki-moon, repeated Tuesday his demand that Israel allow significantly more humanitarian aid into the beleaguered Gaza Strip, and he announced that he would send a team to investigate the bombings of United Nations facilities there.

The human rights organization Amnesty International issued a statement criticizing Mr. Ban for being too timid on the extent of the inquiry.

Mr. Ban said at a news conference that the United Nations was trying to get relief supplies to nearly one million people daily, but that Israel was only allowing one border crossing to open, permitting trucks with supplies for only about 30,000 people to get through.

“We are experiencing serious difficulty in getting all the materials, humanitarian assistance, so it is absolutely necessary that they open the crossings,” said Mr. Ban, whose previous statements urging Israel to allow more aid into Gaza have been ignored. “I will continue to urge that.”