BEIRUT, Lebanon — Iran, Syria’s closest ally, called on the government in Damascus to recognize its people’s “legitimate” demands on Saturday, in the first such remarks to come from the Persian country since the five-month-old uprising against President Bashar al-Assad started.

Although the remarks, by Iran’s foreign minister, Ali Akbar Salehi, did not advocate any specific changes, they were the first public sign of growing unease with the crisis in Syria — even as Iran has maintained an unyielding crackdown on its own dissenters.

Other governments in the region are increasingly worried that the crisis could spill beyond Syria’s borders, especially given Mr. Assad’s seeming determination to snuff out a resilient demonstration movement despite the cost in sectarian and social tensions. That violence continued on Saturday, as Syrian security forces opened fire on hundreds of demonstrators across the country, killing at least three people, according to activists.

“The government should answer to the demands of its people, be it Syria, Yemen or other countries,” Mr. Salehi was quoted by the ISNA news agency as saying. “The people of these nations have legitimate demands, and the governments should answer these demands as soon as possible.”