By Marc Frank

HAVANA (Reuters) - Cuba has ordered some state firms and joint ventures to reduce fuel and electricity consumption, a senior diplomat and the director of a foreign joint venture said on Thursday, in the latest sign a crisis in ally Venezuela is hurting the economy.

While it was not clear exactly what triggered the cuts, Cuba's President Raul Castro warned in December that the economy would go through a rough patch in 2016, citing the impact of low oil prices on the trade relationship with Venezuela.

Cuba has a history of energy rationing, especially in the 1990s after the collapse of the Soviet Union, when the Communist government struggled to survive under a severe U.S. embargo. The current restrictions will not be so severe, but they come at a time when Cubans' expectations are higher thanks to the detente with Washington and economic reforms.

The extent of the rationing, which is expected to take effect in July and be announced next week at a session of the National Assembly, is expected to depend on the sector but there are signs some of the belt-tightening could be quite sharp.

"I saw a copy of the Economy Ministry instructions to the state oil and electricity monopolies yesterday; it stated quotas would be reduced up to 50 percent through the end of the year," the foreign director of a joint venture said on condition of anonymity.

"I called the ministry that supervises our company and they said the level of cuts to our sector were still under discussion," he said.

A statement issued by the Council of Ministers earlier this week said Economy Minister Marino Murillo explained to members the country's economic situation and restrictions being adopted for the rest of the year, without giving details.

"He clarified that those activities that maintain the vitality of the country, in particular those that generate (hard currency) earnings and substitute imports, will be guaranteed," it said, providing no further details.

Low oil prices have taken Venezuela to the brink of economic collapse and destabilized its leftist government, which ships Cuba 90,000 barrels of oil per day as part of an exchange that sends tens of thousands of Cuban professionals to Venezuela.

So far Venezuela seems to be meeting its oil commitments to Cuba although cash payments for doctors and other Cuban professionals have dried up in the past 18 months, experts say.

"There does not seem to have been a cutback in crude oil and or petroleum products deliveries by Venezuela to Cuba, according to marine traffic reports," Jorge Pinon, director of the Latin America and Caribbean Energy Program at the University of Texas, said.

"They may be expecting one in the future, building inventories or simply trying to save money or trying to insure there are no blackouts for residents as electricity demand increases," he said.

Several Western diplomats in Cuba said they received a stream of reports over the last two weeks that the government would cut fuel and electricity quotas to state companies.

"The Cubans are clearly way behind in paying some of our suppliers and now we have these cuts on the horizon," said one commercial attaché who asked not to be identified because of diplomatic sensitivities.

Cuba began cutting back on merchandise imports last year and has been slow in making some payments to creditors and suppliers.

"It is obvious all this has to do with the crisis in Venezuela," he said.

Cuban President Raul Castro told a year-end session of the National Assembly in December that economic growth would slow from 4 percent in 2015 to 2 percent in 2016 due to falling export revenues.

Castro said that lower oil prices had reduced the cost of a number of imports such as food but also hurt "mutually advantageous cooperation relations with various (oil-producing) countries, in particular the Bolivarian Republic of Venezuela."

(Reporting by Marc Frank; editing by Frank Jack Daniel and Richard Chang)