* Benchmark iron ore rebounds from three-week low
* Weak China steel market to limit iron ore price gains
SINGAPORE, July 4 (Reuters) - Price offers for Australian iron ore in top importer China rose on Wednesday after cargoes were sold at higher prices the previous day, although buyers are unlikely to push up rates amid a persistently weak Chinese steel market.
Weak demand in China for steel, however, is likely to keep iron prices soft in coming weeks, analysts say, ahead of the peak demand period in late autumn and early winter.
Offers for iron ore cargoes from Australia, the world's biggest supplier, increased by up to $2 per tonne after miner Rio Tinto Ltd sold 61.5-percent grade Pilbara iron ore fines at higher than market rates on Tuesday.
Rio sold one cargo at $137 per tonne via the platform run by the China Beijing International Mining Exchange, and another through a tender at $137.80, traders said. That was sharply higher than a sale of the same grade in late May at $134.50, and offers of $134-$135 on Tuesday.
"That was a big price to pay given the current market condition, with the outlook for steel consumption remaining weak," said a Hong Kong-based trader.
He said the price increase may have had more to do with the limited spot availability of Australian Pilbara fines over the past two months, rather than a turnaround in the market.
"A lot of people doubt that the price increase will be repeated. Prices of port stocks didn't change. We have a lot of clients saying they would rather wait and see," said a trader in Shanghai.
Other players remained cautious. A seller of above 60-percent grade Ukrainian iron ore concentrate has not quoted prices, and instead wants to see bids from prospective buyer first, said the Shanghai trader.
Benchmark iron ore with 62-percent iron content .IO62-CNI=SI climbed 1.4 percent to $135.40 per tonne on Tuesday, according to Steel Index, recovering from a three-week trough hit the previous day.
Spot iron ore and Chinese steel prices are both down more than 2 percent this year as sluggish steel demand in the world's biggest steel consumer curbs its appetite for the raw material.
China's steel demand will remain soft in July and August, although supply constraints as some mills trim output and increased liquidity available to steel traders will limit the downside price risks, analysts at Mirae Asset Securities said.
"We think Chinese steel demand is likely to pick up after summer, due to late autumn and early winter being the traditional high demand season, improved liquidity flowing into downstream sectors, and key projects starting," they said in a note.
The most-traded rebar contract for October delivery on the Shanghai Futures Exchange was little changed at 4,074 yuan ($640) per tonne by the midday break. ($1 = 6.3523 Chinese yuan)