Snowden, the National Security Agency secrets leaker, was granted temporary asylum in Russia last week. Russia's refusal to extradite him was blamed in part for President Obama's decision to cancel a planned summit with Russian President Vladimir Putin at the Group of 20 meeting next month in Russia.
"Mr. Snowden was a factor, but he was far from the only factor," Carney told reporters at the daily press briefing.
"It certainly remains our position that Mr. Snowden should be returned to the United States where he faces felony charges and where he will be afforded all the rights and protections of defendants in this country."
At the same time, however, "We have a lot of fish to fry ... with the Russians. We have a lot of issues to engage with the Russians over," he said.