* Deepening output cut in Tangshan supports steel prices
* But weaker demand in flood-hit regions curbs gains
* Softer demand seen in some cities due to G20 summit
SHANGHAI, July 25 (Reuters) - Chinese steel futures edged higher on Monday on deepening cuts in output in a key industrial region, although cooling demand due to flooding in some regions helped to curb the gains.
The rise follows a nearly 7 percent drop in Shanghai Future Exchange rebar SRBcv1 last week as investors booked profit on four straight weekly gains and worried over China's slowing property market and its impact on demand for steel products.
Countering worries about demand, Tangshan city in the top steel-producing province of Hebei has deepened mandated output cuts to improve air quality for a memorial day for a 1976 earthquake that killed at least 250,000 people.
The output cuts kicked off on July 12 but the pace has accelerated, traders said.
"The positive news is a bigger output cut, particularly for coking plants, in Tangshan, but demand has also been hit by floods in some regions," said Yu Yang, an analyst with Shenyin & Wanguo Futures in Shanghai.
"The market could be volatile this week."
Benchmark prices for October rebar on the Shanghai Futures Exchange edged up 0.4 percent to 2,352 yuan ($352.23) a tonne by the midday break. The contract fell 6.8 percent last week.
Seventy-two people have been killed and 78 are missing in Hebei province after rain triggered floods and landslides. In central Henan province, 15 people were killed and eight were missing, state media reported on Saturday. said spot steel product prices dropped after the heavy rains affected transportation and sales.
Some analysts also expected steel demand in the world's top producer to be hit by a slowdown and suspension at construction sites in regions near eastern China's Hangzhou city, where the next G20 leaders' summit will be held in early September.
On the Dalian Commodity Exchange, the September iron ore contract DCIOcv1 rose 0.8 percent to 441.5 yuan by midday. Coke DCJcv1 surged more than 4 percent while coking coal DJMcv1 rose over 2 percent.
Iron ore for immediate delivery to China's Tianjin port .IO62-CNI=SI dropped 40 cents to $55.70 a tonne on Friday, according to The Steel Index. The index dropped 3.6 percent last week but has still jumped around 30 percent so far this year.
($1 = 6.6775 Chinese yuan)