Earlier in the day, Axios reported that President Joe Biden discussed a "significant military response" to the attack during a meeting with top US officials on Sunday.
"As for our response options, the President is working his way through that right now. He had a good meeting yesterday with the National Security Team," Kirby told CNN.
According to Axios, the White House and Pentagon are seeking to calibrate their retaliation to contain the risk of a wider conflict. Meanwhile, some hawks on Capitol Hill are pushing for strikes inside Iran, the report said.
"We will respond. We will do it in a time and a manner of our choosing. We’ll respond, you know, in a very consequential way but we don’t seek a war with Iran. We are not looking for a wider conflict in the Middle East," Kirby said, when asked if the US is considering strikes inside Iran.
On Sunday, three US soldiers had been killed and 34 others injured in a drone attack on a US military base in Jordan's northeast near the border with Syria.
President Biden pinned the blame on unspecified Iran-backed militant groups, while also saying the US was still gathering the facts. Jordanian cabinet spokesman Muhannad Mubaidin said that the strike targeted the US's Al-Tanf base in Syria, not a base on Jordanian territory.
Iran has nothing to do with the drone attack on a US military base, Iranian state-run news agency IRNA reported, citing an Iranian official.