Defense Secretary Leon Panetta answers questions during a news conference in Cairo. Panetta is on his first visit to the Middle East since becoming defense secretary. (Win McNamee/AP)

Defense Secretary Leon E. Panetta urged Egypt’s military leadership Tuesday to patch up frayed relations with Israel, make good on promises to build a “legitimate" democracy and release an accused U.S.-Israeli spy.

On each count, Egypt’s military rulers followed their usual custom by saying nothing publicly in response. But Panetta said he came away encouraged that Egypt would remain a “pivotal player in the region” as it unsteadily emerges from a popular revolution that toppled its longtime former president and U.S. ally, Hosni Mubarak.

Panetta, a former CIA director, said he pleaded the case of Ilan Grapel, 27, a dual U.S.-Israeli citizen who was arrested in Cairo four months ago on suspicion of espionage. Egyptian authorities have accused Grapel, an Emory University law student and former Israeli paratrooper, of gathering intelligence for Israel. Grapel’s family and Israeli officials have said he is innocent and that he was volunteering in Cairo for a refugee aid group.

On Monday, during a visit to Tel Aviv, Panetta held out hopes that he would be able to win Grapel’s release. But the law student remained locked up after Panetta left Cairo, and U.S. officials would not say whether they had made any concrete progress in the case.

“We have expressed our concerns about his treatment,” Panetta told reporters at a news conference in Cairo. “We’re confident that ultimately the Egyptian government will deal with that fairly.”

U.S. defense officials said Panetta’s primary mission during his brief stop in Cairo was to encourage Egypt’s military to move ahead with its commitments to hold parliamentary elections starting next month and gradually hand over power to a civilian government.

Panetta said he also pressed Egyptian Field Marshal Mohammed Hussein Tantawi, the chief of the ruling military council, to lift the state-of-emergency law that has largely squelched political activity in the country for three decades. The law gives the government blanket authority to arrest individuals and was used by Mubarak to stifle opponents.

The Egyptian military has pledged repeatedly to lift or modify the law, as did Mubarak, but has shied away from saying when it will do so. U.S. officials have said they are concerned that the legitimacy of the upcoming parliamentary elections could be undermined if the law remains in place for much longer.

Panetta said Tantawi reassured him that the military intends to repeal the law. U.S. defense officials, however, said the Egyptians again would not commit to a date.

“I did make the request that I thought it was important that they lift the emergency law,” Panetta said. “The response I got back is that they are seriously looking at the first opportunity to be able to do that. I said it was important to be able to lift it if we’re going to proceed toward free and fair elections in Egypt. They agreed with that.”

The Obama administration has sought to reaffirm its relations with Egypt after decades of backing Mubarak, who is now on trial on charges of corruption and the unlawful killing of protesters. Despite calls from some members of Congress to limit military aid to Egypt until it elects a civilian government, the Obama administration has counseled patience.

It has also taken care not to be seen as lecturing Tantawi or his deputies, noting Egyptian sensitivities toward what they perceive as outside interference. As a result, Panetta was full of praise during his visit and avoided direct criticism.

“I really do have full confidence in the process that the Egyptian military is overseeing,” he said. “I think they’re making good progress.”

Although polls show the military remains broadly popular among Egyptians, dissent is growing among demonstrators who ousted Mubarak. Those critics say the military is interfering with nascent political movements and has been vague about how, if and when it will cede power to a civilian government.

“I don’t think any of these decisions are clear yet, and I don’t think, frankly, the military knows,” Anne Patterson, the U.S. ambassador to Egypt, said at the news conference with Panetta.