* Draft law would give government tighter control over gas supplies
* European, U.S. firms would also be allowed to operate gas infrastructure
* Russia cut off supplies last month in row over unpaid bills
* Country on brink of energy collapse, says PM
(Adds PM's quotes, background)
KIEV, July 4 (Reuters) - Ukraine's parliament gave preliminary approval on Friday to a draft law that would allow the Kiev government to exert tighter control over the energy sector in the face of dwindling natural gas supplies after Russia cut off exports last month.
The parliament also approved, in a first reading, a bill that would allow consortiums with European or U.S. companies to operate Ukraine's ageing gas distribution system and storage facilities.
"Russia is trying to tighten as many screws as possible on us," Prime Minister Arseny Yatseniuk told parliament, urging it to give his government the right to declare a "state of emergency" in the energy sector.
"A gas war has been rolled out against us. The country is on the brink (of energy collapse)."
Russia, Ukraine's main supplier of gas as well a of natural gas for Europe via Ukraine, cut off supplies to the ex-Soviet republic on June 16 in a dispute over unpaid bills.
It has also hinted it will take retaliatory trade measures against Ukraine over its signature last month of a free trade deal with the European Union.
Parliament initially rejected the government's energy proposals, but resumed discussion and took a vote on the two draft laws on Friday after speaker Oleksander Turchynov warned that without them many homes could be left without heating in winter.
"There is a risk for millions of our citizens. This is a question of survival," he warned.
Yatseniuk, urging cooperation with European or U.S. companies in operating the Soviet-era gas pipeline system, said this would bring structural modernisation essential for Ukraine given Russian plans to build a gas pipeline system that would bypass Ukraine.
"Adoption of this law opens the way to Ukraine to become an energy player," Yatseniuk said.
Some deputies on Thursday had voiced fears over possible retaliation from Russia if it were not given the same access to Ukraine's gas infrastructure as would be offered U.S. and European firms.
Russia had previously offered to buy into Ukraine's gas distribution system in return for cheaper gas.
The draft laws on possible "state of emergency" powers would give the government the right to dictate to gas companies to whom they should supply gas and for how much, irrespective of supply obligations under existing contracts.
The proposed legislation appeared to apply to private gas companies as well as the state gas and oil company Naftogaz, Ukraine's biggest gas importer.
The draft laws are expected to go to parliament for a second reading at the end of July or in August.
(Writing by Richard Balmforth; editing by Jason Neely)