MUNICH/STUTTGART, Germany (Reuters) - German carmaker Daimler (>> Daimler AG) said on Thursday it will step up cost-cutting efforts as it wants to see its premium Mercedes-Benz brand catch up with more profitable rivals Audi and BMW.

In the next phase of its "Fit for Leadership" programme, the company will target cost reductions and efficiency gains exceeding the 2 billion euros (1 billion pounds) seen in the first phase from 2012 to 2015, Chief Executive Dieter Zetsche said.

"But what is even more important is that this will help us ready the company for the next 10 and 20 years, so it's not just about a billion more or less," he told analysts at the company's investor day.

He did not say how long the second phase would be or when it would start.

Zetsche has been slimming down Daimler to try and make it more efficient since Volkswagen-owned Audi (>> Volkswagen AG) overtook Mercedes in 2011 to become the world's second-biggest luxury carmaker by vehicle sales, behind BMW (>> Bayerische Motoren Werke AG).

Mercedes has already come a long way. In the first quarter of 2015, it posted a return on sales - including its smart, AMG and Maybach sub-brands - of 9.2 percent, only just below the 9.5 and 9.7 percent posted by BMW and Audi, respectively.

Its global deliveries jumped 18 percent to 459,708 cars in the three months, although still behind BMW's 526,669 and Audi's 497,073. Daimler said on Thursday it had now, for the first time in a decade, overtaken BMW and Audi everywhere except in China, the world's biggest auto market.

Zetsche was more bullish than rivals on growth in China, where car sales slipped in April and May, saying he expected Mercedes' deliveries there to grow by a double-digit percentage this year.

BMW by contrast warned last month that the market slowdown in China was hitting premium carmakers harder than other players and said it had cut production there.

Audi's CEO Rupert Stadler said earlier this year he expected China's car market to grow by up to 9 percent this year and said Audi should keep up well with that pace.

Many automakers have responded by slashing prices, but Mercedes-Benz cars sales' chief, Ola Kaellenius, said his company's discount levels in China had been flat over the past 12 months.

"Some of our competitors have moved in the other direction. But we have been there before and it is not a happy place," he said at the investor day.

Mercedes has also just opened an Indian factory to cut costs and boost sales.

(Reporting by Edward Taylor and Ilona Wissenbach; Writing by Maria Sheahan; Editing by Susan Fenton)

Stocks treated in this article : Bayerische Motoren Werke AG, Daimler AG, Volkswagen AG