The rouble-dollar rate reached 66.7 on the Moscow stock exchange.
Sergei Skripal and his daughter Yulia survived nerve-agent poisoning in Britain after spending weeks in hospital.
Relations between Russia and the West hit a new low, and the USA was among United Kingdom allies that expelled Russian diplomats.
Peskov highlighted on Thursday what he called the "unpredictability of Russia's partners across the Atlantic.you can expect anything from Washington", he told CBS News partner network BBC News, calling the USA, "an unpredictable worldwide player". "So linking these events is unacceptable to us, and just as with previous USA sanctions we believe are absolutely illegal and against worldwide law", Peskov told reporters.
Prices steadied a little on Thursday, with US crude edging down 13 cents to $66.80 per barrel and Brent flat at $72.27.
The State Department's surprise announcement of the new sanctions on Wednesday jolted Moscow, where some politicians and analysts had been hopeful that Putin's meeting with President Trump in Helsinki in July would stabilize U.S. These are sensitive goods that normally would go through a case-by-case review before they are exported. These could go as far as a ban on Russian airlines using U.S. airports. The first, which targets U.S. exports of sensitive national-security related goods, comes with deep exemptions and numerous items it covers have already been banned by previous restrictions.
Under US legislation, the administration is obliged to act once there has been a determination that chemical or biological weapons have been used. Authorities determined that they had been attacked with a military-grade Russian nerve agent known as Novichok. Since the chances of this determination being made are nearly a certainty, the next round of sanctions is coming in three months.
All are prohibited from any transactions involving the U.S. financial system.
Russian Federation has repeatedly denied responsibility for the attack, and Russia's embassy in Washington said in a statement that the US State Department's findings against it in the case were not backed by facts or evidence. Those sanctions restrict travel and financial transactions.
Moscow has angrily rejected any involvement in the poisoning, plunging diplomatic relations with London into crisis.
The Kremlin said the new sanctions were "illegal and do not correspond to global law".
The sanctions enacted so far this year, and the threat of more, have already inflicted pain on Russia's middle class.
What was the nerve agent?
The New Zealand dollar dropped 1.1 percent to a two-year trough at US$0.6665 after the country's central bank pledged to keep rates at record lows well into 2020. More than 20 countries expelled Russian envoys in solidarity with the United Kingdom, including the US. Washington ordered 60 diplomats to leave and closed the Russian consulate general in Seattle.
Two other British citizens fell ill due to Novichok exposure in late June in a town close to Salisbury. Three months later a British woman, Dawn Sturgess, died after being poisoned by novichok in a...