US Defense Secretary Robert Gates, seeking to soothe Mideast allies worried about Teheran's reach, said Sunday that efforts to bolster US relations with Iran may still ultimately face what he called "a closed fist." Gates was flying to Egypt, the first stop on a Mideast tour that continues in Saudi Arabia. He said part of his mission will be to assure Saudis that any US outreach to Iran aims to increase security throughout the region. Building diplomacy with Iran "will not be at the expense of our long-term relationships with Saudi Arabia and the other Gulf states that have been our partners and friends for decades," Gates told reporters aboard a military jet headed to Cairo. "There's probably some concerns in the region that may draw on an exaggerated sense of what's possible," Gates said. "And I just think it's important to reassure our friends and allies in the region that while we're willing to reach out to the Iranians, as the president said, with an open hand, I think everybody in the administration, from the president on down, is pretty realistic and will be pretty tough-minded if we still encounter a closed fist." Gates will arrive in Cairo on Monday and will be in Riyadh, the Saudi capital, on Tuesday. He also noted concerns throughout the Mideast about Iran's influence in Baghdad, and said they could be staved off if more Arab nations opened embassies or otherwise became more involved in Iraq. Gates praised Egypt, for example, for having "taken some serious steps forward to re-engage." Critics of Iraqi Prime Minister Nouri al-Maliki accuse him of forging ties with fellow Shi'ites who are allied with Iran. The issue has been a flashpoint for Iraq's Sunnis, who, under Saddam Hussein, fought Iran decades ago. Negotiations between Israel and the Palestinians will be a major topic for Gates and Egyptian President Hosni Mubarak when the two men meet in Cairo early Tuesday. Gates credited Egypt as working as a go-between between the two sides. Gates said discussions in Riyadh would include US efforts to have Yemeni detainees now being held at the Navy prison at Guantanamo Bay, Cuba, rehabilitated in Saudi facilities. An estimated 100 of the 241 Guantanamo detainees are Yemeni. The US is reluctant to release them to Yemen, where convicted terrorists have escaped from prisons. But the Yemeni government has so far balked at agreeing to send the Yemeni detainees to Saudi Arabia. "Clearly there will be an interest in pursuing that with them," Gates said. Gates also welcomed any help Saudi officials could give to Pakistan's fragile government. "The Saudis in particular have considerable influence in Pakistan," he said. "And so I think that whatever they can do to bring Pakistanis together in a broader sense to deal with the challenge to the government in Islamabad obviously would be welcome."