The new EU punitive measures came into effect on Friday and targeted major state firms as well as one of president Vladimir Putin's closest allies, Sergei Chemezov, a technology magnate.
New US sanctions, meanwhile, hit Russia's top bank as well as leading energy and technology companies.
Restrictions on the Russian oil firms were designed to shutdown offshore oil exploration projects in the Arctic, the Reuters news agency quoted a senior US official as saying.
The rouble slumped to a new record for a second day, retreating to 37.93 against the US dollar as of 1225 GMT, while Moscow stock markets fell.
Sergey Lavrov, Russia's foreign minister, said the sanctions hurt chances of creating lasting peace in war-torn Ukraine.
"We believe that adopting such decisions at the very moment when the peace process in Ukraine is gaining strength ... this means choosing a path towards undermining the peace process."
"We will react in a calm and adequate manner, first and foremost proceeding from the need to protect our interests," Lavrov said on the sidelines of the Shanghai Cooperation Organisation in Dushanbe.
A ceasefire signed last Friday between Kiev and separatist rebels in Ukraine's east seems to have largely held fast so far.