(Adds comment from U.S. lawmaker, background, paras 10-11)

WASHINGTON, Jan 8 (Reuters) - The United States is ready to give technical aid to help Egypt stop arms smuggling into Hamas-run Gaza, but Cairo must improve border patrol efforts, U.S. Secretary of State Condoleezza Rice said on Tuesday.

Israeli officials have complained that Egypt is doing a "terrible" job on the Gaza border, failing to stop smuggling of weapons and ammunition into Gaza through tunnels under the so-called Philadelphi Corridor that separates Egypt and Gaza.

"We think that Egypt has to do more. Those tunnels need to be dealt with," Rice said in an interview with Middle East journalists in Washington before traveling to the region with President George W. Bush.

A U.S. Army Corps of Engineers team has studied the problem and talked to Egyptian security personnel about it, Rice said.

"The Egyptians have said that they want some, perhaps, technical help. We're prepared obviously, to give that, but it's also -- you know, the will to do it is very important here," Rice said.

Islamist Hamas took control of Gaza in June, prompting Israel to tighten its military and economic cordon around the coastal territory.

But last month, Israeli officials said they had sent a videotape to Washington showing Egyptian security forces helping Hamas militants smuggle arms across the border into Gaza.

The Egyptian government says it is doing its best with the personnel it is allowed to deploy at the border under the 1979 peace treaty and a subsequent agreement with Israel.

"The Egyptians need to deal with it. We're going to try to help them deal with it," Rice said in a transcript of the interview released by the State Department.

Rep. Steve Israel of New York, a Democratic lawmaker who saw Egyptian President Hosni Mubarak earlier this week, said Cairo wanted to redirect $23 million of U.S. aid to Egypt for equipment to detect the tunnels used for smuggling into Gaza.

Congress voted last month to withhold $100 million of planned military aid to Egypt until Egypt made progress on several fronts, including improving security on the border with Gaza.

Israel pulled troops and settlers out of Gaza in 2005, but still controls key crossing points, airspace and coastal waters.

Sen. George Voinovich, an Ohio Republican who just returned from a Middle East trip, told U.S. reporters "one of the reasons the Egyptians have a problem with the border is, they want to make sure that humanitarian aid gets into Gaza."

Bush and Rice were leaving later on Tuesday for a weeklong tour of Israel and Arab countries, including Egypt, aiming to nurture fragile Israeli-Palestinian peace efforts. (Editing by Eric Beech)

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