By Nichola Groom

LOS ANGELES, Nov 19 (Reuters) - Nissan Motor Co Ltd said it will lift U.S. production of its all-electric Leaf as demand for the car has surged sharply this year following a cut to its sticker price.

For many automakers, demand for electric vehicles has generally failed to live up to expectations set when models like the Leaf and General Motors Co's gasoline-electric hybrid Volt were being developed.

But Jose Munoz, Nissan's senior vice president of sales and marketing for the Americas, said the Leaf is now the top reason customers are referred to the Nissan brand, adding that the vehicle is profitable.

"From a purely attraction and branding point of view it's already a very good car," he told reporters at the NADA/J.D. Power Western Automotive Conference in Los Angeles. The event was being held in conjunction with the L.A. Auto Show.

The automaker dropped the U.S. price of the Leaf by more than $6,000 to $29,650 at the beginning of this year after a shift in production of the model to the United States from Japan allowed it to cut manufacturing costs.

Munoz said the company was still weighing exactly how much it will boost output at the Smyrna, Tennessee plant where it produces the Leaf, but added it would be "an important increase."

Nissan is selling more than 2,000 Leafs a month in the United States. It sold 18,078 Leafs to U.S. drivers from January to October, not far behind the 18,782 Chevrolet Volts delivered in the same period and a big jump from the 9,819 sold in all of 2012.

Supplies of the Leaf at U.S. Nissan dealers are currently running at about 20 days. Normally the company likes to keep supplies at around 60 days.

"We are supply constrained... We will start producing more Leafs probably by the end of this year -- so December January time," he said.

Munoz was promoted to lead Nissan's North American business this month as part of a broad management shakeup at the company. He takes on his new role Jan. 1.

Munoz' comments came the same day U.S. auto safety regulators launched an investigation into electric car maker Tesla Motors' Model S sedan after three car fires in six weeks, including two in the United States..

Munoz said Tesla's recent troubles had not impacted sales of the Leaf.