* Q4 Weakest sales since Q1 2010
* Recovery seen in second half of 2013
* ASML shares reverse fall, up 6.7 pct (Adds quotes from CFO, analyst, bullet points)
By Anthony Deutsch
VELDHOVEN, Jan 17 (Reuters) - ASML, the world's leading provider of tools for making computer chips, warned that its sales in 2013 would be virtually flat, due to weaker orders and stalling demand for personal computers.
ASML, which has been investing heavily in new technology to enable electronics makers to make smaller chips, said its sales fell 17 percent in the fourth quarter, the lowest level since the first quarter of 2010.
New orders for the machines used by the top makers of smart phones, computers and other devices to create electronic wafers came in at 667 million euros, well below a market forecast of 800 million euros.
ASML's shares fell initially fell as much as 4.7 percent on its weak outlook but later rose as much as 7 percent as analysts pointed to ASML's new production technology, its dividend increase and possible share buyback programme.
"ASML could potentially implement a 700 million euro buyback," said Credit Suisse in a research note.
The stock was up 6.7 percent at 51.23 euros by 1604 GMT.
ASML, which derives its revenue from a mix of traditional computer memory chips and chips used in hand-held tablets and smart phones, said full-year sales would be roughly 4.7 billion euros.
It said the first quarter would be weak because of slow sales in the PC market and the cost of investment in EUV, or extreme ultraviolet, light technologies for making next generation, smaller chips which are not yet on the market.
A pick up in the market in the second half of the year will offset the weak first quarter, but most likely not enable it to grow its annual sales, it said.
The Dutch firm, considered a barometer for the tech sector, reported better-than-expected net profit of 298 million euros ($396 million) on sales of 1.02 billion euros, largely thanks to a tax benefit. Analysts in a Reuters poll had forecast profit of 185 million euros on sales of 1.029 billion euros.
ASML, whose customers include Samsung Electronics , Taiwan Semiconductor Manufacturing (TSMC) and Intel Corp, said the driver for a recovery in the second half would be chips used in smartphones, tablets and other mobile gadgets.
"There is not a lot of anticipation for PC growth this year. We will basically see a continuation of what we saw in 2012," chief financial officer Peter Wennink said. The transition to using newer chips could drive slighter higher sales.
"The PC market will remain a very important indicator for us. The overall market will pick up in the course of the year," he said.
ASML said it would continue to return money to investors through dividends, and would announce a new share buyback programme next month after shareholders in Cymer Inc - a supplier of lithography light sources used to make chips - approve ASML's takeover offer.
It said it expected to get a 700 million-euro boost from pre-sales of EUV tools this year, and added the memory sector could also see a recovery later in the year.
The quest to produce ever smaller, more efficient, more powerful chips pushed ASML into two important deals last year.
It agreed to buy Cymer in order to speed up the development of its tools using EUV, and also secured funding from Intel, Taiwan Semiconductor Manufacturing, and Samsung for the research and development of EUV technology and of equipment for making larger wafers. (Reporting by Anthony Deutsch, writing by Gilbert Kreijger; Editing by Sara Webb and Sophie Walker)