Washington sanctioned 13 individuals and 12 entities on February 3 after the White House put Iran "on notice" over a ballistic-missile test and other activities.
The Treasury Department posted a listing, naming the individuals and the companies added to the sanctions list.
It was unclear if Spicer was referring to the Houthi suicide attack on a Saudi navy patrol with three suicide boats near the Yemeni port of Hodeidah on Monday, killing two Saudi sailors, or Iran's seizure of 10 USA sailors from patrol boats in January 2016.
Some of the newly sanctioned groups are based in the United Arab Emirates, Lebanon and China.
The sanctions order comes a day after National Security Adviser Michael Flynn said the White House was putting Iran "on notice".
President Obama had previously agreed to lift sanctions on Iran, after it halted its nuclear programme - but Trump has previously spoken about his contempt for the agreements.
"The Trump administration condemns such actions by Iran that undermine security, prosperity, and stability throughout and beyond the Middle East and place Americans lives at risk", Flynn said.
"I think we also need to ratchet up sanctions". "You are going to see an effort to really change the terms of this over time".
"With the increase in sanctions, the perception that the United States might be rolling back on the Iran deal - and the anti-Iran mood that is emerging in Washington - will further empower hardliners in Iran, where the rhetoric will be, "we told you so - these people can not be trusted", said Maha Yahya, director of the Carnegie Middle East Centre.
The government confirmed on Wednesday that it had test-fired a new ballistic missile on Sunday.
Foreign Minister Javad Zarif tweeted Friday that his country was "unmoved by threats as we derive security for our people".
Asked if he's willing to consider a military option, Trump said Thursday that "nothing is off the table".
One reason Mattis was on the outs with the Obama administration is that he supported tougher responses to Iranian mischief in the region.
Iran has test-fired various ballistic missiles since its July 2015 nuclear deal with world powers and it's unclear, from a technological standpoint, what is different about the latest launch. At some points, Trump vowed to strictly police the agreement.
"Iran continues to threaten the USA friends and allies in the region", Flynn said.