"In our view, these and earlier restrictions are absolutely unlawful and don't conform to global law", Peskov said.
USA and European allies have publicly blamed the Kremlin for attempting to kill the two in the British town of Salisbury using a Novichok nerve agent, a claim Russian President Vladimir Putin has denied.
The new sanctions will take effect on or around 22 August.
Sergei Skripal, a former colonel in Russia's GRU military intelligence service, and his 33-year-old daughter, Yulia, were found slumped unconscious on a bench in Salisbury in March after a liquid form of the Novichok type of nerve agent was applied to his home's front door.
The Kremlin has repeatedly denied the allegations, while the United Kingdom authorities have provided no proof of Russia's involvement in the case.
That breach automatically triggers the imposition of sanctions and places requirements on Russian Federation to avert further restrictions in three months' time.
Dawn Sturgess, 44, later died in hospital.
Trump has not shied away from condemning the Skripal attack, but critics have questioned why it has taken the US government so long to impose the new sanctions in response.
The second tranche, which can be selectively activated after 90 days if Moscow fails to provide "reliable assurances" it will no longer use chemical weapons and blocks on-site inspections, is potentially more serious.
Zakharova said the United States was "knowingly presenting demands that are unacceptable to us" as conditions for the sanctions to be lifted.
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Julia Leveridge released a statement Monday that read, in part, that "while The Ohio State University has never contracted Ms. Smith to discuss these allegations, she will fully cooperate with the university's current investigation".
"The UK welcomes this further action by our USA allies", a No 10 spokesman said. He insisted that Russia's financial system is strong enough to withstand shocks from the new penalties.
If Moscow violates the sanctions then it could see restrictions on flights from the Russian Aeroflot airline to the US, sanctions on USA bank loans, increased export and import restrictions, including on gas and petroleum, and potentially even a downgrade of diplomatic relations. Russian blue-chip stocks plunged as much as 9%, led by state banks and national airline.
Several members of Congress had expressed concern that the Trump administration was dragging its feet on the determination and had missed a deadline to publish its findings.
Republican Representative Edward Royce of California, chairman of the House Foreign Affairs Committee, in a letter sent to Trump shortly after the Skripal attack, said he was encouraged by the joint statement Trump signed with allies. British police scoured sections of Salisbury and Amesbury in southwest England, searching for a container feared to be contaminated with traces of the deadly nerve agent Novichok.
"The mandatory sanctions that follow this determination are key to increasing pressure on Russian Federation".
"Let us welcome the United Sanctions of America!"
The US response may be partly motivated by a desire to be seen to be tough on Moscow after accusations that Mr Trump was too soft on Russian Federation. His administration has sanctioned a number of Russian officials and oligarchs for human rights abuses and election meddling.
The decision, he said, was aimed at the American audience who viewed the president as soft on Mr Putin.
A senior State Department official said Wednesday that there could be exceptions.