UPDATE 2-Japan Oct-Dec steel output seen down 4 pct yr/yr

* Output seen up 3.7 pct from July-Sept -trade ministry

* Demand seen down 0.1 pct on yr, up 5 pct on qtr

* January-March outlook remains uncertain (Adds graphic, estimated export volume in paragraph 6)

By Yuko Inoue

TOKYO, Sept 29 (Reuters) - Japan's crude steel output is set to recover in the October-December quarter to near its year-earlier level, driven by exports and a pick-up in the auto and construction sectors, the trade ministry said on Tuesday.

Japanese steelmakers, including the world's No.2, Nippon Steel Corp (5401.T), and No.5, JFE Holdings Inc (5411.T), have been boosting production as the industry pulls out of its worst slump in decades on improving exports to China and other Asian countries.

Automakers are also boosting orders for steel as government stimulus measures help car sales.

Crude steel output is expected to fall 4.2 percent to 25.28 million tonnes in the October-December quarter from a year earlier, the Ministry of Economy, Trade and Industry said. But it would be up 3.7 percent on the preceding quarter.

Battered by the global financial crisis, Japanese crude steel output plunged 43 percent in the year's first quarter from a year earlier and 39 percent on the year in the second.

For the trend in Japan's steel output, click: here

The ministry expects exports to hit a record 6.8 million tonnes in the year's fourth quarter, up 40 percent from a year ago, as strength in the economies of China and other Asian countries provides a short-term boon for Japanese steelmakers.

That would account for 35 percent of estimated crude steel demand during the quarter.

Steel demand from carmakers will almost recover to its level a year earlier in the quarter, while demand from the construction and engineering sectors will improve sharply as government stimulus measures filter down to the sector.

But the longer-term outlook remains cloudy, the ministry said.

"The outlook for the export market and the government's stimulus measures remain uncertain," said Masaki Koito, a director at the ministry.

"Possible oversupply in Asia adds to that concern," he said, citing Chinese and some Asian countries' plans to increase production capacity.

Demand for steel from construction companies and manufacturers in the period from October to December is seen totalling 19.48 million tonnes, down 0.1 percent from a year earlier but up 5 percent on the prior quarter, the ministry said. (Editing by Clarence Fernandez)