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* STOXX 600 up 0.2%

* Miners top gainers on China stimulus hopes

* Generali rises as investor gets nod to hike stake

* Euro zone factory downturn deepens in June

July 3 (Reuters) - European shares gained on Monday, boosted by gains in Italy's biggest insurer Generali after investor Delfin received a regulatory nod for a stake increase, while hopes of more policy stimulus from China also lifted sentiment.

The pan-European STOXX 600 index was up 0.2% by 8:29 GMT, kicking off the first day of the second half of the year on an upbeat note.

Shares of Assicurazioni Generali hit their highest in over a year and were last up 5.0% after news that Italy's insurance regulator had authorised investor Delfin to raise its stake to above 10% in the company sparked anticipation that an investor battle for control will resume.

Shares of Mediobanca, which counts Delfin as its single biggest shareholder, rose 2.5%.

The moves helped Italy's financials-heavy benchmark FTSE MIB climb 0.9%, surpassing other bourses in the region, which were up between 0.1% and 0.4%.

The index was at its highest since 2008 - a level it also hit on Friday.

The broader STOXX 600 had gained 8.7% in the first half of the year, largely due to strong gains early into 2023. However, the rally petered out later as China's weak economic recovery and evidence of slowing growth in the euro zone took a toll on sentiment.

Fresh reports on Monday painted a dour picture of the euro zone economy, with a survey showing manufacturing activity in the region contracted faster than initially thought in June, as persistent policy tightening by the European Central Bank squeezed finances.

"On the one hand (data) clearly shows growing weakness in the European economy. But it also suggests that (it) will bring inflation down and that the European central bank's interest rate hikes are having the impact they need," said Danni Hewson, head of financial analysis at AJ Bell.

Italy's manufacturing sector contracted in June at the steepest rate in over three years, a separate report showed on Monday while France's manufacturing sector continued contracting, though the decline was slower than expected.

Miners were the top sectoral gainers, up 1.6% as most metal prices rose on hopes that China's government will deliver a stronger economic stimulus package after a survey showed the country's factory activity slowed in June. Limiting gains, shares of AstraZeneca dropped 4.2% after the British drugmaker noted some adverse events in its lung cancer drug trial. (Reporting by Amruta Khandekar in Bengaluru and Matteo Allievi in Gdansk; Editing by Nivedita Bhattacharjee and Janane Venkatraman)