Mr Kirby was speaking to Qatar-based broadcaster Al Jazeera after the release of four Americans from Iran's notorious Evin prison into house arrest.
"We are not in talks with Iran on the Joint Comprehensive Plan of Action [JCPOA]," he said when asked about other US-Iran files being addressed through mediators.
"This is not on the agenda now."
Mr Kirby said Washington was focusing on bringing the released Americans, in addition to one other who was already under house arrest, back to the US.
Iran is set to receive $6 billion of its funds from South Korea, which had been frozen since 2019 when the previous US administration under Donald Trump pulled sanctions waivers on countries importing Iranian oil. The money is in a restricted bank account.
The US pulled out of JCPOA with Iran in 2018. The Biden administration has been engaging in indirect talks, alongside EU officials, to return to the agreement, which would limit Iran's nuclear capabilities while lifting US sanctions on the country,
Last year, EU officials repeatedly suggested an agreement was close but talks fell through when the sides reached a stalemate.