At a joint press conference with Japanese Foreign Minister Masahiko Komura on Wednesday evening, Rice said she hoped the case will not harm the countries' ties.
"I did begin my discussion with the Foreign Minister by expressing the regrets of the United States. I earlier had had a chance to express the regret to the Prime Minister on behalf of President Bush, of behalf of myself and of the people of the United States for the terrible incident that happened on Okinawa."
The recent arrest of the Marine on suspicion of raping a 14-year-old girl on the island, as well as some previous ones, has inflamed popular anger at the US military presence.
Rice was in Tokyo on the third and last leg of her Asian tour that has been dominated by the North Korea issue.