Energy Minister Aleksandr Novak said in statement today that "Russia is introducing a pre-payment regime for gas deliveries to Ukraine," starting June 1 after Ukraine missed a May 7 deadline to pay off its $3.5 billion gas debt.
Ukraine pledges to pay off the debt but Kyiv objects to the new price that Russian state-owned gas company Gazprom is charging it for gas supplies.
In March, after former Ukrainian President Viktor Yanukovych was ousted, Gazprom raised the price it charges Ukraine for gas from $285 per 1,000 cubic meters to $485.
The announcement of pre-payment rules for Ukraine came on the same day that Lithuanian officials announced Gazprom would cut the price it charges Vilnius for gas by more than 20 percent.
Authorities have discouraged public gatherings, fearing they could spark clashes between pro-Russian activists and supporters of Ukrainian unity.
Ukrainian Prime Minister Arseniy Yatsenyuk said on May 8 that he suspects Russian President Vladimir Putin was planning some form of "skirmish" to discredit Kyiv as the country celebrates the 69th anniversary of the defeat of Nazi Germany in 1945.
Yatsenyuk spoke after pro-Russian separatists in Donetsk and Luhansk in eastern Ukraine said they will go ahead with referendums on self-determination on May 11 despite calls by Putin to postpone them.
Putin's spokesman said the Kremlin needed more information about the rebels' decision.
A spokeswoman for EU foreign-policy chief Catherine Ashton said the referendums "should not take place neither on May 11 nor any other later date."
U.S. Deputy Secretary of State William Burns said Russia was heading down a "dangerous and irresponsible path" and the situation in Ukraine was "extremely combustible."
Burns spoke after NATO again said it had seen no Russian withdrawal of troops along the border with Ukraine as Putin has vowed to do.
Elsewhere, some 40 armed men attacked a Ukrainian post on the Russian frontier on May 8.
The Ukrainian border guard said the attackers were beaten off by Ukrainian forces.
Meanwhile, Ukrainian leaders have proposed the creation of a "Round Table" to resolve the crisis in the country.
The announcement was made on May 8 by Yatsenyuk and acting President Oleksandr Turchynov.
The round table, the two leaders said, would draw in political forces and civil groups in all regions, with international mediators asked to help.
Analysts say the Ukrainian plan includes many elements of a draft "Road Map" to peace presented on May 8 in Kyiv by the Swiss chair of the Organization for Security and Cooperation in Europe (OSCE).
Efforts to defuse the Ukraine crisis were also discussed by Russian Foreign Minister Sergei Lavrov and U.S. Secretary of State John Kerry in a telephone conversation on May 8.
Early morning in #Odessa lots of police in the empty streets. Looks like the new police chief is doing everything to prevent violence today
— Petr Shelomovskiy (@stopnarcotics) May 9, 2014
US will run series of military drills with elite special op forces in Estonia,Latvia & Lithuania scheduled this month http://t.co/9ibqpYtv32
— Ryskeldi Satke (@RyskeldiSatke) May 9, 2014
US-NATO air presence tripled in Estonia,Latvia & Lithuania since Russian invasion of Ukraine https://t.co/J7WDYZPoqL pic.twitter.com/qoMdrCwVfV
— Ryskeldi Satke (@RyskeldiSatke) May 9, 2014
"#Donetsk People's Republic" insist logistics in place for Sunday referendum. Voting to be held in hospitals, schools, official buildings.
— Douglas Herbert (@dougf24) May 9, 2014
A huge turnout with an hour still to go to the first parade. pic.twitter.com/i2Cg7tjp3W
— Daniel Sandford (@BBCDanielS) May 9, 2014
Ukraine refuses Russian demand for advance gas payment http://t.co/2PyKlmXfv9
— bruce springnote (@BSpringnote) May 9, 2014
On Red Square the open top Zils are ready for Russia's military bosses. Victory Day parade this morning. pic.twitter.com/HzK6Z6CrGA
— Steve Rosenberg (@BBCSteveR) May 9, 2014
Among the things he said was that strong will of the Russian people, their resilience, saved Europe from slavery.
He also said Victory Day is a source of patriotism, sorrow, and pride for the Russian people.