(Adds TEPCO forecasts, details)

TOKYO, July 20 (Reuters) - Japanese trade minister Akira Amari said on Friday industry would need to restrict electricity use during peak periods after a powerful earthquake forced the shutdown of the world's biggest nuclear power plant.

Tokyo Electric Power Co. (TEPCO) <9501.T>, the operator of the Kashiwazaki-Kariwa plant in northwestern Japan, said it had enough capacity to meet demand without firing up expensive oil-fired back-up generators, with help from other utilities unless summer was unusually hot.

But the minister said industrial restrictions would be needed to ensure a safe margin in supplies.

TEPCO, Asia's largest utility, said it had asked Japanese oil refiners to supply extra fuel oil but added it now had enough fuel to power up six mothballed thermal plants, if needed.

In a report to the ministry, TEPCO said it could meet electricity demand in July and August with assistance from other utilities, if the maximum summer temperature did not go over 35.3 degrees Celsius (96 Fahrenheit) -- a temperature that Tokyo sometimes reaches in summer.

However, the utility said there was a risk of a shortage if high temperatures prompted an unsusual spike in demand or if there was further trouble at generating facilities.

TEPCO said it could supply a peak of 66.54 million kilowatts of electricity capacity in July and 62.14 million kilowatts in August with help from other power companies.

This was enough to cover its forecast peak demand for the months of 61.11 million kilowatts, which is based on temperatures staying below the 35.3 degrees Celsius mark.

The nuclear plant closed after Monday's earthquake has a capacity of 8.2 million kilowatts, around 12 percent of TEPCO's estimate of peak summer demand in Tokyo.

Of the total, TEPCO said it would be able to supply up to 59.7 million kilowatts to meet peak demand in July and 58.01 million in August, even without the closed nuclear plant.

TEPCO has asked for help from six utilities to meet demand and said on Wednesday it might approach others.

The six companies it has already asked were: Tohoku Electric Power Co. <9506.T>, Kyushu Electric Power Co. <9508.T>, Chugoku Electric Power Co.<9504.T>, Shikoku Electric Power Co. <9507.T>, Chubu Electric Power Co. <9502.T> and Kansai Electric Power Co. <9503.T>.

Market sources said the fuel oil sought by TEPCO would be used to generate power at back-up thermal plants during the summer peak. Two refiners -- Japan Energy Corp. and Cosmo Oil Co. <5007.T> -- said they will sell extra fuel oil to TEPCO.

It is the first evidence of increased oil demand that traders have been expecting since the government ordered TEPCO to keep its Kashiwazaki-Kariwa plant closed.

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