MEDELLIN, Colombia, Jan 24 (Reuters) - Egypt must ensure the security of its border on the Gaza Strip where militants have blown a hole in the wall built by Israel, U.S. Secretary of State Condoleezza Rice said on Thursday.

"I understand that it's a difficult situation for them. But it is an international border. It needs to be protected and I believe that Egypt understands the importance of doing that," Rice told reporters before arriving in Medellin on a trip to promote a free trade agreement with Colombia.

Rice blamed Hamas, which controls the Gaza Strip, for the situation that led to the destruction on Wednesday of a 200-year (200-metre) section of the 20-foot-high (6-metre-high) metal border wall.

"This problem has come first and foremost out of the security situation created by Hamas in Gaza and they're unwillingness to stop -- and I'm quite certain they could if they wished to -- the rocket fire against, against Israel," Rice said.

"With that said, the innocent people of Gaza are in a very difficult situation and we've stressed with the Israelis to do everything that they can to allow humanitarian aid to continue," Rice said.

Rice said that Israel had been responsive to the humanitarian concerns raised by the United States.

Israel, which occupied the Gaza Strip in 1967, pulled troops and settlers out in 2005 but still controls its northern and eastern borders, airspace and coastal waters. It has imposed a blockade that it says is meant to counter militant rocket fire.

Deputy Defense Minister Matan Vilnai said on Thursday Israel wanted to wash its hands of Gaza altogether by handing over the supply of electricity, water and medicine to others. An Israeli security official said Egypt should take over responsibility.

"We need to understand that when Gaza is open to the other side we lose responsibility for it. So we want to disconnect from it," Vilnai said.

(Editing by Cynthia Osterman)

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