The strikes by US warplanes and cruise missiles targeted the Islamic State movement as well as the little-known Khorasan group, which Washington said has said was plotting attacks against US targets.
"We think the strikes had an impact, important impact," Rice told NBC news, 36 hours after Washington expanded its bombing campaign from Iraq to Syria, backed by allies in the region.
"Obviously, this won't be the last of our efforts. But this was a first wave."
Rice said the United States at this point is unable to confirm that the airstrikes succeeded in killing Khorasan's alleged leader, long-standing Qaeda operative Muhsin al-Fadhli.
"We can't confirm that at this stage. We've seen reports on social media to that effect. We will continue to look for signs as to whether or not that's, in fact, the case," Rice told NBC.
The coalition aims to destroy the Islamic State group, which controls a swath of territory in Iraq and Syria, has murdered two US journalists and a British aid worker and is locked in a brutal war with Iraqi and Kurdish authorities.