* Operating profit 1.049 bln eur vs poll avg 969 mln
* To increase capacity 3-3.5 pct this year
* Aims to cut costs by at least 1.5 pct this year
* Unit revenue fall slows in January
* Shares rise 7 percent, pulls sector higher (Adds shares, industry context, analyst)
By Victoria Bryan and Cyril Altmeyer
BERLIN/PARIS, Feb 16 (Reuters) - A "resilient" start to 2017 from Air France-KLM and a better than expected operating profit lifted shares in the airline to their highest level since July on Thursday.
But Air France-KLM management and sector analysts cautioned against reading too much into the latest figures, given the challenges facing the airline and its rivals.
"We are not euphoric, we are cautious, that's why we're continuing to work on costs," Chief Financial Officer Frederic Gagey told journalists following the results.
Long-haul bookings, where Air France-KLM has said it wants to regain market share, were satisfactory so far this year, Gagey added. The airline, which restricted 2016 capacity growth to 1 percent, wants to grow by 3 to 3.5 percent this year.
European airlines are battling to bring down costs to compete with budget rivals such as Ryanair and easyJet , prompting strikes at Lufthansa, Air France and British Airways in recent months.
Overcapacity in Europe is also weighing on ticket prices, posing headaches for all the region's carriers.
The Franco-Dutch carrier said that while there was a high level of uncertainty around ticket revenues, unit revenue had fallen by just 0.7 percent in January, compared with a 5 percent drop for 2016 as a whole.
Air France-KLM shares rose as much as 7 percent in response to the 34 percent jump in 2016 operating profit to 1.049 billion euros and the January bookings update.
Gagey said a 1 percent cut in unit costs - how much it costs the airline to operate in terms of seats and kilometres flown excluding the effects of fuel - last year was "significant" for Air France-KLM, which has struggled with strikes and fraught relations with its unions.
By comparison, Ryanair, which has the lowest cost base of Europe's airlines, reduced costs by 6 percent in its quarter.
Industry consultant John Strickland said "legacy" carriers such as British Airways owner International Consolidated Airlines Group and Lufthansa had understood they needed to take action in order to compete with the low cost carriers, with IAG so far making the most progress.
Gagey said Air France-KLM was aiming to reduce costs by at least 1.5 percent this year with initiatives such as a new Air France unit, dubbed Boost, that will operate at lower costs out of its hub at Charles de Gaulle in Paris.
Pilot costs would be cut by 15 percent and cabin crew by 40 percent under the proposals, which were greeted with scepticism by pilots' unions when presented by Air France last week.
While KLM had an operating margin of 6.9 percent in 2016, Air France's was just 2.4 percent, which Gagey said was due to strikes by Air France pilots and cabin crew and the impact of Islamist militant attacks on French tourism.
Editing by Sudip Kar-Gupta and Alexander Smith