BEIJING, May 17 (Reuters) - Chinese construction rebar and hot rolled coils (HRC) futures declined on Monday, down for a third consecutive session after steel prices powered to historical highs last week and led regulators to step up inspections.

Data on Monday also showed record monthly crude steel output in China for April despite government's efforts to encourage cuts to production.

Surging steel prices have forced some construction firms to slow metal purchases while some exporters hurt by rising commodity prices have had to pass on increased costs to customers.

Regulators in the cities of Shanghai and steel hub Tangshan on Friday also warned local mills against price gouging, collusion or other irregularities that might disrupt market order, which is expected to help keep a lid on prices.

The most-traded steel rebar on the Shanghai Futures Exchange , for October delivery, fell 2.8% to stand at 5,599 yuan ($869.75) per tonne as of 0330 GMT. That compares with a record closing high of 6,171 yuan on Wednesday.

Hot rolled coils used in the manufacturing sector tumbled 4.4% to 5,992 yuan a tonne. It marked a record closing high of 6,683 yuan on Wednesday.

Fitch Ratings said in a note that it expects "the rally in China's steel price to slow in coming weeks as summer approaches, as the season tends to see lower downstream demand due to subdued construction activity."

It added that high prices for iron ore and new environmental curbs could keep steel prices elevated.

Benchmark iron ore futures on the Dalian Commodity Exchange , for September delivery, jumped 1.2% to 1,201 yuan a tonne.

Dalian coking coal futures rose 1.6% to 1,975 yuan per tonne and coke fell 1.2% to 2,629 yuan.

The July contract for stainless steel on the Shanghai bourse increased 1.8% to 15,405 yuan per tonne.

($1 = 6.4375 Chinese yuan) (Reporting by Min Zhang and Shivani Singh; Editing by Edwina Gibbs)