The 55-year-old is believed to have paid $50,000 (£32,000) to hunt a lion in Zimbabwe's largest game reserve, but he says he was unaware it was so famous.
"If I had known this lion had a name and was important to the country or a study obviously I wouldn't have taken it," Mr Palmer said. "Nobody in our hunting party knew before or after the name of this lion."
Cecil was well known in the Hwange National Park and was being tracked with a GPS collar as part of a research programme run by Oxford University.
The Zimbabwe's safari organisation has said the way in which Cecil was lured out of a national park was unethical and possibly illegal.
Initially, Zimbabwe sought to charge and extradite Mr Palmer, but the government's interest in him has waned in recent weeks.
The Associated Press news agency reported that government officials fear it could hamper a hunting industry that is lucrative and important for the country.