Putin told the new ambassador that bilateral relations with the United States "at their current level can not be viewed as satisfactory".
Kremlin spokesman Dmitry Peskov warned people Monday that unauthorized rallies will have consequences for the people responsible. "There have been certain problems with reciprocity so far". The incumbent Vladimir Putin has yet to announce his candidacy but is widely expected to do so and to win.
Relations between Russian Federation and the United States cooled following Russia's annexation of Crimea in 2014 and its support for separatists in eastern Ukraine, where fighting since 2014 has left 10,000 people dead.
Anatoly Antonov replaced Sergei Kislyak, who was mired in allegations of spying and interfering in the 2016 US election.
Putin also described the mass shooting as "shocking in its cruelty" in a message to U.S. President Donald Trump on Monday.
Huntsman said at his confirmation hearing that there was no question Russian Federation interfered during the 2016 campaign.
He was the nation's top diplomat to Singapore under President George HW Bush and ambassador to China under President Barack Obama before returning to the USA to run for president in 2012.
His successor, career diplomat John Tefft was summoned out of retirement and served as United States ambassador to Russian Federation between 2014 and 2017.
Huntsman, a businessman, veteran diplomat and former presidential candidate, came to Russian Federation at a tense time, when the White House-Kremlin diplomatic relations are at a dangerously low ebb.
"I look forward to working to rebuild trust between our two countries and to strengthening the bilateral relationship based on cooperation on common interests", he said in a statement released by the U.S. Embassy.