A written statement the White House released before Earnest spoke said the U.S. remained committed to finding and bringing home Levinson, who is from Coral Springs, Florida.
"We respectfully ask the government of the Islamic Republic of Iran to assist us in securing Mr. Levinson's health, welfare, and safe return," the statement said.
Hekmati's sister Sarah Hekmati said Tuesday that she and her family hope more frequent discussions between U.S. and Iranian officials lead to her brother's release after more than two years.
"We feel more reassured that Amir's case can be raised now with this bridge that's been built ... and we can be closer to a resolution," she said.
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Associated Press writer Jeff Karoub in Detroit contributed to this report.