Russia retaliated against tough new Western sanctions on Thursday, banning most food imports from the United States and the European Union and threatening to block flights over its airspace.

The 28-member European Union swiftly denounced the measures -- which also target Canada and Australia -- and said it was ready to take action in response.

Ukrainian authorities said Thursday they had closed three checkpoints on the border with Russia after nightly assaults by separatists.

The move came as the government vowed to beef up its security presence to counter pro-Russian rebels, amid reports of continued fighting in the country's east.

Russian Prime Minister Dmitry Medvedev will visit Crimea during Ukraine's presidential vote on Sunday as Moscow demonstrates its hold over the peninsula it annexed in March.

Among other meetings during the two-day visit, Medvedev will on Sunday visit immigration offices in the city of Sevastopol where Russian passports are being issued to local residents, his office said in a statement.

Russia and Western powers are on the brink of a new Cold War over the crisis in Ukraine, Russian Prime Minister Dmitry Medvedev said in an interview broadcast Tuesday.

"Basically we are slowly but surely approaching a second Cold War that nobody needs," Medvedev said in an interview with Bloomberg Television that was also published on the Russian government's website.

Russia is ready to face a new round of Western sanctions over Ukraine, Prime Minister Dmitry Medvedev said Tuesday.

"I am sure we will be able to minimize their consequences," he said in a televised speech to parliament.

Prime Minister Dmitry Medvedev visited Crimea on Monday, the first Russian leader to travel to the Black Sea region after Moscow seized it from Ukraine.

"Am in Simferopol. Today the government will discuss the development of Crimea," Medvedev wrote on Twitter.

Ukraine's deposed president Viktor Yanukovych is still the legitimate head of state of the country even if his authority is "negligible", Russian Prime Minister Dmitry Medvedev said Monday.

Medvedev added that Russia does not recognize the new authorities who took power in Kiev after the overthrow of Yanukovych, saying they had violated the constitution.

Moscow pledged Tuesday it would not intervene in the crisis in neighboring Ukraine but said the country should not be forced to choose between Russia and the West.

"We confirmed our principled position of non-intervention in Ukraine's internal affairs and expect that everyone follows similar logic," Foreign Minister Sergei Lavrov said.

More than 60 protesters died from gunshot wounds on Thursday in fresh clashes between thousands of demonstrators and heavily-armed riot police in the heart of Kiev, a medic who works with the opposition said.

"More than 60 protesters died today. They all have gunshot wounds," the EuroMiadan Medical Center coordinator Svyatoslav Khanenko told Agence France Presse.

Caretaker Prime Minister Najib Miqati discussed with Russian President Vladimir Putin the latest developments in the region and the bilateral ties between the two countries.

Miqati, who is currently in Russia, also held talks with his Russian counterpart Dmitry Medvedev on the sidelines of his visit to the country to attend the opening of the winter Olympic opening ceremony in Sochi.