Washington has not commented publicly on reports the three were kidnapped by an Iranian-backed Shiite militia, but Kerry confirmed he had raised the case with Tehran.
"I've raised it with Foreign Minister Zarif," Kerry told reporters at the World Economic Forum in Davos, Switzerland.
"I asked him ... if Iran knew any way to provide help or if there were some way they could have an impact on getting the right kind of outcome," he added.
"He said he would take that under advisement and try to do what he can. He didn't have any immediate knowledge whatsoever about it."
Iraqi authorities are searching for the three Americans, whom the Baghdad security command said were seized last week from a "suspicious apartment" in south Baghdad.
Iraqi officials have dubbed the case a kidnapping, but US officials still speak cautiously of a "disappearance," in what could become a politically explosive case.
The three were allegedly taken just as Kerry and Zarif were finalizing the implementation of the Iran nuclear deal and the release of five US prisoners held in Iran.
If one of the Iranian-backed militias that operate in Iraq was responsible for a kidnapping this would feed the anger of US critics who see both deals as a capitulation.
Opponents of President Barack Obama's outreach to Iran argue he has been naive about the ongoing threat Tehran poses to US interests and its regional allies.
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