The tweets from Pushkov, chairman of the Information Policy Committee in Russia's upper house of parliament, came a day after US Secretary of Defense James Mattis
and US Secretary of State Rex Tillerson
commented on Russia while attending summits in Europe.
Pushkov tweeted early Friday: "Trump hopes to make a deal with Russia. Mattis thinks (in vain) that he can put pressure 'from a position of strength'. Tillerson is playing a 2nd Kerry. Three lines from 1 administration."
Speaking Thursday after a NATO conference in Brussels, Belgium, Mattis said the United States was "not in a position right now" to collaborate with Russia on military matters and spoke of the need to negotiate with Russia "from a position of strength."
He also accused Russia of violating international law, labeling its actions as "aggressive" and "destabilizing," and said there was "very little doubt" that Russia had interfered or attempted to interfere in a number of democratic elections.
Tillerson reassures allies
Meanwhile Tillerson, needing to reassure European allies concerned by Trump's stated desire for improved relations with Moscow
, took a more middle-of-the-road stance on Russia while at a G20 summit in Bonn, Germany.
The top US diplomat -- who took over the role from Secretary of State John Kerry -- said the United States would consider working with Russia on some issues, but that it would also stand up for its allies, including on the side of Ukraine, whose Crimea territory was annexed by Russia in 2014.
Tillerson, who spoke as he met Russian Foreign Minister Sergey Lavrov for the first time, called on Moscow to deescalate continuing violence in eastern Ukraine
and said Russia needed to "honor its commitment to the Minsk Agreements" -- a European-brokered ceasefire plan signed in Minsk, Belarus, in 2015.
Trump himself did little to assuage concerns about his administration's approach to Russia during a press conference
Thursday, held in a week during which questions over his aide's ties to Russia dominated the headlines.
Trump's national security adviser Michael Flynn resigned
Monday amid a controversy over his contacts with the Russian ambassador to the United States. CNN later reported
that high-level advisers close to Trump were in constant communication during the summer election campaign with Russians known to US intelligence.
Trump said during the news conference that as far as he knew, none of his staff had been in contact with Russian officials, adding that media stories on the subject were "fake news."
Moscow: 'More important' things to do
Asked Friday about Trump's news conference, a Kremlin spokesman said Moscow had "more important" things to do than to watch it.
"Listen, the Kremlin has so many domestic affairs to deal with, and these affairs are way more important for us than a press conference by the US president," spokesman Dmitry Peskov said during a conference call with journalists.
"Therefore we don't have the abilities or intentions to watch every press conference of the US President, with all due respect."
In his tweets, Pushkov also warned that the US President would be dragged into the "Washington swamp," a reference to Trump's populist campaign message that he would "drain the swamp" by uprooting the establishment.
"It's highly likely that it won't be Trump draining the 'Washington swamp' but the swamp itself will drag in Trump. And that will be the end of his revolution that never started," Pushkov tweeted.