CAIRO—Iran and Egypt's new government signaled Monday they were moving quickly to thaw decades of frosty relations, worrying the U.S., Israel and Saudi Arabia that the overtures could upset the Mideast's fragile balance of power.

Iran said it appointed an ambassador to Egypt for the first time since the two sides froze diplomatic relations more than three decades ago, the website of the Iranian government's official English-language channel, Press TV, reported late Monday.

Also Monday, officials at Egypt's Ministry of Foreign Affairs confirmed that new foreign minister Nabil Elaraby is considering a visit to the Gaza Strip—an area controlled by Hamas, a militant Palestinian Islamist group backed by Tehran and until now shunned by Cairo.

The announcements follow a rare meeting earlier this month between a high-level Iranian diplomat and Mr. Elaraby, after which the foreign minister told reporters that Egypt has "opened a new page" with Iran.