Mr Huntsman arrived in Moscow on Sunday to take over from John Tefft, who left after serving in Russian Federation for three years, a period marred by a deep and rapid deterioration of ties, unseen since the end of the Cold War.
The spokeswoman called the US campaign a "huge mistake", adding that Moscow had never expelled foreign journalists from Russian Federation by revoking their accreditation or ending their visas.
"We are ready to build cooperation with the Latvian Republic in the spirit of good-neighborly relations, taking into account each other's interests. And Moscow continues to meddle in the democratic processes of our friends and allies".
State-run RIA Novosti news agency reported that Muscovites laid flowers outside the U.S. Embassy in Moscow.
Putin's spokesman Dmitry Peskov said earlier Tuesday that the Russian president wanted to restore ties with the United States but stressed he could not do it alone.
"So far, there are problems with reciprocity", Peskov.
After he announced his presidential bid past year, Navalny, arguably Russia's most popular opposition politician, inspired a grassroots campaign in Russian regions to support his nomination.
Russian officials initially voiced confidence that Trump's election would help improve ties, but those hopes appear to have faded substantially as the U.S. Justice Department and congressional committees investigate Moscow's alleged interference in the election and seek to determine whether associates of Trump colluded with Russia.
"The current level of the ties can not satisfy us", Mr Putin said.
The US sent a new ambassador to Russia, Jon Huntsman arrived in Moscow on Monday to take over from John Tefft, who left after serving in Russia for three years. Moscow denies such activity and Trump dismisses any talk of collusion.