* Iron ore, coke and coking coal jump more than 2 pct
* Supply glut, slowing demand still weigh on steel prices (Updates close prices)
By Ruby Lian and David Stanway
SHANGHAI, May 20 (Reuters) - Chinese steel futures edged up on Friday, but rising output and seasonal weakness in demand in the world's top consumer of the metal keep pressuring prices.
Steel prices have lost more than a quarter from the 2016 high hit in April as investors turned cautious over the economic recovery in the world's second-largest economy.
The market has also been pressured as the rally that began in December prompted some closed mills to restart, slowing efforts by Beijing to cut the sector's overcapacity.
"Steel mills are still in the process of recovering production, which has lent support to raw materials, but the rising supplies of steel and waning demand in May and June will hit steel prices," said Yu Yang, an analyst with Shenyin & Wanguo Futures in Shanghai.
"Some investors are taking advantage of the mild rebound, but the overall steel market has downside risk."
The most-traded rebar futures contract on the Shanghai Futures Exchange SRBcv1 edged up 0.7 percent to 2,062 yuan ($315.15) a tonne by close.
Dalian iron ore futures DCIOcv1 closed 1.4 percent higher at 375 yuan a tonne. Both steel and iron ore futures posted a modest weekly gain after three continuous weeks of losses.
Coking coal and coke are better supported than iron ore due to tight supplies as the Chinese government has reined in coal production. Conversely, top Australian and Brazilian miners have maintained high production of iron ore.
Dalian coking coal DJMcv1 climbed 2.8 percent and coke DCJcv1 jumped 2.5 percent by close. ($1 = 6.5430 Chinese yuan renminbi)