Medvedev said Russia would have to look at its financing for defense and security measures in light of the pressure being put on it.
"If our partners carry on sanctions, we'll take measures against foreign companies and people in response," he warned. "These sanctions won't help Ukraine."
His words echoed a warning by Russian President Vladimir Putin on Wednesday that the sanctions are already harming ties between his nation and the United States.
"They generally have a boomerang effect and, without a doubt, in this case, are driving the Russian-U.S. relations into a stalemate and seriously damaging them," he said, according to a Kremlin transcript of his remarks to reporters on a visit to Brazil.
"I am certain that this is harmful to the U.S. Administration and American people's long-term strategic national interests."
He accused the United States of pushing Ukrainian authorities toward a continued conflict, whereas Russia wants to see an immediate end to hostilities and a negotiated solution involving all sides, he said.
Financing squeeze, assets freeze
Announcing the sanctions Wednesday at the White House, Obama said, "We have to see concrete actions, and not just words that Russia in fact is committed to trying to end this conflict along the Russia-Ukraine border."
With the new sanctions, "what we are expecting is that the Russian leadership will see once again that its actions in Ukraine have consequences, including a weakening economy and increasing diplomatic isolation," he said.
The expanded U.S. measures target two Russian banks -- Gazprom Bank and VEB -- and two energy companies -- Novatek and Rosneft.
They will not be able to get new medium- and long-term financing in the United States, senior administration officials told reporters in a conference call.
In addition, the new sanctions freeze any U.S. assets and prohibit American business contacts for eight Russian arms companies that make weapons, including small arms, mortars and surface-to-air missiles. One of the eight is the Kalashnikov Concern, maker of the AK-47 assault rifle and other arms.
Also on the list: Four Russian government officials, including the minister of Crimean affairs; the self-styled Luhansk People's Republic and Donetsk People's Republic leading the separatist campaign in eastern Ukraine; and Aleksandr Borodai, the self-declared "Prime Minister" of the Donetsk group.
Targeting the separatist groups that simulate government structures prevents them from seeking financing, the senior administration officials noted.
A statement published on the EU website Wednesday said the European Council would decide by the end of July on which entities and individuals to target with expanded sanctions over their actions in Ukraine.
The council also asked the EU Commission to reassess EU-Russia cooperation programs, with a view to deciding, on a case-by-case basis, on suspending their implementation.
"The European Council urges the Russian Federation to actively use its influence over the illegally armed groups and to stop the flow of weapons and militants across the border, in order to achieve a rapid deescalation," the statement said.
Earlier this year, the United States and Europe imposed a range of sanctions in response to Russia's annexation of Crimea this spring and massing of troops along Ukraine's eastern border. The earlier sanctions included asset freezes and travel bans.