"Your compliance with the Chemical and Biological Weapons and Warfare Elimination Act of 1991 is critical to showing Putin that we are serious about challenging his deadly acts, as well as his ongoing attacks on our democracy".
"Our American friends must understand this".
The Kremlin responded by describing the sanctions as illegal and unfriendly and adding that the U.S. move was at odds with the "constructive atmosphere" of Mr Trump and Mr Putin's meeting in Helsinki last month.
The move was announced today by the USA state department.
That could include the USA withdrawing support for worldwide loans and US bank loans, blocking Russian airlines from landing in the USA, and suspending diplomatic relations.
Medvedev said that while the US says that the sanctions are meant to punish Russia's "bad" behavior, their real goal is to sideline a rival.
Kremlin spokesman Dmitry Peskov called the new sanctions "categorically unacceptable" and "illegal".More news: Tottenham make history by completing no summer signings
The Russian Embassy in Washington said the "draconian" new sanctions against Russia weren't backed by any facts or evidence, noting that while the USA said it has enough information to conclude that Russia is to blame, it refused to disclose what it has, saying the information is classified.
Last month, British Prime Minister Theresa May urged Trump to raise the issue of the poisonings when he met with Russian President Vladimir Putin in Helsinki, although it remained unclear whether the subject came up in their talks.
The warning, from Prime Minister Dmitry Medvedev, reflects Russian fears over the impact of new restrictions on its economy and assets, including the rouble which has lost almost six percent of its value this week on sanctions jitters.
The State Department's announcement fuelled already worsening investor sentiment about the possible impact of more sanctions on Russian assets and the rouble at one point slid by over one per cent against the dollar, hitting a two-year low, before recouping some of its losses.
The warning by Prime Minister Dmitry Medvedev came after Washington unveiled a raft of new sanctions against Russian Federation over its alleged use of the Novichok nerve agent against a former double agent which Britain has blamed on Moscow.
The Russian rouble has slumped to its lowest level since November 2016, hours after the USA announced new sanctions because of the poisoning of an ex-Russian spy and his daughter in the UK.
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.
"They are not an instrument, but the policy itself".
The prospects for passage of what Graham called the "sanctions bill from hell" are uncertain.