White House spokesman Josh Earnest also said the United States "certainly would condemn any country that's carrying out mass executions" and warned that the dispute between Tehran and Riyadh would make it more difficult to push warring side in the Syrian conflict towards a political solution.
"There have been direct concerns raised by US officials to Saudi officials about the potential damaging consequences of following through on the execution -- on mass executions, in particular, the execution of" the Shi'ite cleric Nimr al-Nimr, Earnest told a news briefing.
"This is a concern that we raised with the Saudis in advance, and unfortunately, the concerns that we expressed to the Saudis have precipitated the kinds of consequences that we were concerned about," he said.
Shi'ite communities around the world reacted furiously to the execution of Nimr, whom Earnest described as a political opposition figure and religious leader. Protesters in Tehran set fire to the Saudi embassy and the kingdom cut diplomatic relations with Iran, its Shi'ite regional rival.
"We do continue to be concerned about the need for both the Iranians and the Saudis to de-escalate the situation. We are urging all sides to show some restraint and to not further inflame tensions that are on quite vivid display in the region," Earnest said.
He said US Secretary of State John Kerry had been in touch with his Iranian counterpart and US diplomatic officials had been in contact with Saudi officials to convey the message.
Earnest said the United States had regularly raised concerns about the human rights situation in Saudi Arabia, including in conversations between President Barack Obama and Saudi King Salman.
The flare-up between Iran and Saudi Arabia threatened to derail efforts to end Syria's five-year-old civil war, where Saudi Arabia and other Gulf Arab powers support rebel groups against Iranian-backed President Bashar al-Assad.
"It was very difficult to get everybody around the table. It certainly is going to be even more difficult to get everybody back around the table if you have the Saudis and the Iranians trading public barbs and public expressions of antagonism between the two countries," Earnest said.