Peskov criticised the US decision to link the sanctions to the British nerve agent case, an incident the Kremlin has long cast as a Western plot to damage its reputation and provide a pretext for more sanctions.
Former Russian spy Sergei Skripal and his daughter were poisoned by Novichok, a military-grade nerve agent, in Salisbury in March.
The latest USA action follows the Treasury's imposition of sanctions in March against 19 Russian citizens and five entities for interfering in the 2016 U.S. election - the toughest steps against Moscow since Trump took office.
Mr Skripal and his daughter Yulia were in intensive care for several weeks after being poisoned with the chemical substance at his home in Salisbury in March.
"We are being threatened with further escalation of sanctions pressure", she said.
Vladimir Vasilyev, a senior researcher at the Institute of the United States and Canada in Moscow, said the Americans were strengthening sanctions "from an element of pressure into an ultimatum".
New sanctions against Russian Federation will be imposed later this month for illegally using a chemical weapon in an attempted assassination of a former spy and his daughter in Britain earlier this year, the United States said.More news: US Ambassador’s vehicle attacked in Dhaka
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U.S. airlines could be prevented from using Russian airspace and the supply of rocket engines crucial to launching new satellite cut off under measures being considered in the Kremlin as retaliation for the surprise announcement of new sanctions. "And it's unlikely they're in any way associated with the complicated but constructive atmosphere of the last meeting between the two presidents".
However, the department says it will exempt aid to civil society and humanitarian groups and allow exports needed for continued U.S. -Russia cooperation in space. He said the new sanctions amount to "inflicting a punishment in the absence of a crime, in the tradition of lynch law".
According to USA media reports, the new measures include a ban on granting licenses to export sensitive national security goods to Russian Federation.
The State Department announced the sanctions on Wednesday.
European countries and the United States expelled 100 Russian diplomats after the attack, in the strongest action by Trump against Russia since he came to office.
NBC, citing USA officials, said the second round of sanctions could include downgrading diplomatic relations, suspending the state airline Aeroflot's ability to fly to the United States and cutting off almost all exports and imports.
In early April, just before the first tough round of US sanctions in response to Russian "worldwide malign activity" was announced, the ruble stood at roughly 58 to the dollar. The United Kingdom blamed Russia for the attack, resulting in the expulsion of 150 Russian diplomats from the U.K., U.S. and other allies.
Police think the novichok was sprayed or smeared on their front doorknob with a perfume bottle.
Russian lawmaker Sergei Ryabukhin made the remarks Thursday, saying Moscow could cut off supplies of the RD-180 rocket engines to the U.S.