UPDATE 1-Dalian iron ore hits 14-week peak, backed by firmer steel

* Spot iron ore back above $60/tonne for first time since May

* Iron ore inventory at mills and ports declines -Morgan Stanley

* Shanghai rebar touches two-week high (Updates prices)

MANILA, Aug 2 (Reuters) - Iron ore futures in China extended their recent gains to hit a 14-week high on Tuesday as firmer steel prices encouraged producers to buy the raw material.

That should continue to strengthen bids for physical iron ore cargoes and lift the benchmark spot price further above $60 a tonne, traders said.

“Mills are profitable so they continue to raise their production to catch up with the good market,” said a Shanghai-based iron ore trader.

“For the moment, they’re willing to buy high-quality raw material so they can increase their production rate.”

The most-active September iron ore contract on the Dalian Commodity Exchange closed up 2.8 percent at 485.50 yuan ($73) a tonne after peaking at 489 yuan earlier, the highest since April 25.

Iron ore for delivery to China's Tianjin port .IO62-CNI=SI climbed 2.9 percent to $60.50 a tonne on Monday, its strongest since May 4, according to The Steel Index.

Morgan Stanley said iron ore inventory at small- and medium-sized Chinese mills dropped 0.4 percent on July 28 from July 14, with the average number of days of usage down two to 28.

Inventory of the raw material at China’s ports decreased 0.5 percent from the prior week to 105.6 million tonnes as of July 29, following five weeks of increases, Morgan Stanley said in a report.

Steel prices sustained recent gains that had been supported by tightness in Chinese supply as floods in the northern part of the country disrupted transport routes and environmental inspections across some provinces forced the closure of some facilities.

“But the supply side is now getting back to normal so the upside risk to steel prices may be limited,” said the Shanghai trader.

The most-traded rebar, a construction steel product, on the Shanghai Futures Exchange closed 2 percent higher at 2,514 yuan a tonne. Earlier in the day, it hit 2,529 yuan, its loftiest since July 18.

Inventory of rebar at 28 major Chinese cities rose 2 percent from the prior week to 3.5182 million tonnes as of July 29, according to data tracked by SteelHome consultancy. SH-TOT-RBARINV

Rebar stockpiles dropped to 3.4235 million tonnes in mid-July, the lowest since at least December 2011.

$1 = 6.6461 Chinese yuan Reporting by Manolo Serapio Jr.; Editing by Subhranshu Sahu and Biju Dwarakanath