SHANGHAI (Reuters) - China's drug regulator said on Thursday it will strengthen oversight of clinical trials of new drugs, where it said regulation was falling short despite a recent push to improve the quality of local drugs and compete better with international rivals.

The China Food and Drug Administration has rejected dozens of drug applications over the past few months due to false or incomplete trial data. A further 82 firms withdrew applications earlier this month.

China, the world's second-biggest drugs market behind the United States, is pushing an ambitious program of healthcare reforms to improve its home-made medicines and reduce reliance on generic and more innovative drugs from overseas.

The drug regulator said in a statement on Thursday that while some regions had made progress in cracking down on poor drug trial data, many regions were still falling behind.

"The inspection work in some regions is not being taken seriously enough and the quality of inspection is too low," the regulator said, adding it had recently done spot checks on clinical trial bodies and in many cases found false and incomplete data.

China's crackdown on poor quality drugs follows a call in July for manufacturers to carry out their own internal investigations into trial data, which had already led to a number of voluntary recalls.

Global drugmakers in China are facing a tough challenge as local firms get increasingly competitive and as the central government looks to rein in drug prices to help curtail a wider medical bill expected to hit $1.3 trillion by around 2020.

The top 10 Chinese drugmakers have seen sales grow around 12 percent this year, according to data from IMS Consulting, twice the rate of international rivals whose sales have slowed since a bribery scandal at GlaxoSmithKline two years ago.

(Reporting by Adam Jourdan; Editing by Christopher Cushing)