Zimbabwe police are hunting a traditional spirit medium who led President Robert Mugabe's government on a fruitless search for much-needed fuel she said was mysteriously oozing out of a rock.

The southern African state is battling with acute fuel shortages amid an economic crisis many blame on Mugabe's policies.

On Sunday, a Zimbabwean government newspaper reported a 35-year-old traditional healer and spirit medium claimed to have discovered diesel streaming from a rock in the northwest around Chinhoyi Caves, protected by locals as a traditional shrine.

Rotina Mavhunga had said "the diesel was a gift from ancestral spirits who saw that their children were suffering because of the fuel shortage" and was pictured by a local newspaper holding a hosepipe stuck into a rock, "spewing the oil," the Sunday Mail said.

Mugabe's governing ZANU-PF dispatched an investigation team, including three senior cabinet ministers, which established there were no oil fields, the Sunday Mail quoted the party's information secretary Nathan Shamuyarira as saying.

"The team reported to the (ZANU-PF) politburo that there was no need to pursue the issue as nothing convincing had been found, meaning that there were no deposits of diesel in the area," Shamuyarira said.

Police spokesman Wayne Bvudzijena was not available for comment. But the Sunday Mail quoted him and other officials as saying Mavhunga and her people had angered authorities with their false claims.

The Sunday Mail said Mavhunga was on the run following the arrest of more than 50 of her disciples "for failure to prove the existence of fuel".

The false oil discovery tale itself demonstrates Zimbabwe's desperation in the face of a deep crisis that has also left the once-prosperous country struggling with chronic food shortages, no foreign currency reserves for imports, and the highest inflation rate in the world of over 4,500 percent.

The fuel problems have at times forced public transport operators to pull vehicles off the road, forcing thousands of urban commuters to walk to work.

On Thursday, Mugabe's government announced it was banning private fuel purchases in foreign currency, apparently in a bid to tackle black market trading in the fuel sector.

But the country's central bank governor Gideon Gono has warned the ban risked strangling the already battered economy, currently reeling from a controversial price blitz.

Mugabe, 83 in power since independence from Britain in 1980, ordered a price slash three weeks ago, charging that businesses were hiking prices in support of a Western-sponsored plot to overthrow his ZANU-PF government.

Mugabe says Zimbabwe's economic crisis is a result of sabotage by opponents trying to punish him for the seizure and redistribution of white-owned farms to landless blacks.

Analysts say Mugabe's latest policies would further hurt the economy, but were part of his short-term goal to retain power in general elections due next March.