BEIJING, July 1 (Reuters) - Activity in China's manufacturing sector expanded slightly in June though not as much as expected, an official survey showed on Wednesday, offering some signs that the world's second-largest economy may be starting to level out after a raft of support measures.

The official Purchasing Managers' Index (PMI) stood at 50.2 in June, even with the previous month's reading. Analysts polled by Reuters had predicted it would edge up to 50.3.

But growth remained tepid, with the reading just above the 50 point level that separates contraction from expansion on a monthly basis.

The flash HSBC/Markit PMI released last week showed factory activity contracted for the fourth straight month in June but at a slower pace, suggesting the economy may have stopped losing steam, albeit there is no sign of a recovery.

The central bank cut lending rates on Saturday for the fourth time since November and trimmed the amount of cash that some banks must hold as reserves, stepping up efforts to support the slowing economy.

The government is due to release second-quarter GDP data on July 15 and many economists expect growth to dip below 7 percent, which would be the weakest performance since the global financial crisis.

Weighed down by a property downturn, factory overcapacity and high levels of local debt, China's economic growth in 2015 is seen slowing to around 7 percent - the weakest annual expansion in a quarter of a century.

(Reporting by Kevin Yao; Editing by Kim Coghill)