The two world leaders are due to meet face-to-face in Geneva on June 16. Sergei Ryabkov, Russia’s deputy foreign minister, warned Washington to expect “uncomfortable” signals between now and the summit in Switzerland.
He said: “The Americans must assume that a number of signals from Moscow… will be uncomfortable for them, including in the coming days.”
His stark message comes 24 hours after Mr Biden said he would press Mr Putin to respect human rights.
Relations between Moscow and Washington remain strained over the treatment of Kremlin critic Alexei Navalny, an increased military presence in Ukraine, as well as allegations of election hacking, something Russia denies.
Defence Minister Sergei Shoigu also fired shots across the Atlantic and warned the US-Nato alliance had recently increased military activity to the West of Russia, which required a response from Moscow.
Mr Shoigu stated Russia is prepared to take “adequate countermeasures”.
He said: “The actions of our Western colleagues are destroying the world’s security system and force us to take adequate countermeasures,” the Interfax news agency quoted Shoigu as saying.
“Around 20 military formations and units will be formed in the Western Military District by the end of the year.”
“It is obviously meant to exert pressure, to create a negative backdrop for the summit – in a bid to gain political points on the topics that might be discussed by the two presidents.”
Last month, the Kremlin banned eight officials from European Union, including Mr Sassoli, from entering Russia after the bloc imposed sanctions on Russian citizens.
The European Parliament President said no sanctions or intimidation would stop the parliament or him defending human rights, freedom and democracy.