Sellers of imported iron ore cargoes in China cut prices for a third day on Tuesday as weak demand pushed down the benchmark rate to a one-week low, as the near-term outlook for the steel market remained weak despite recent gains.

Price offers for iron ore from Australia, Brazil and India dropped by another $1-$2 per tonne, according to Beijing-based consultancy Umetal.

That followed a 2.5 percent fall in the benchmark 62-percent grade iron ore .IO62-CNI=SI to $103.70 per tonne on Monday, the weakest since Sept. 14, based on data from information provider Steel Index.

Iron ore has recovered from a near three-year low of $86.70 reached earlier this month, on hopes that China's approval of more than $150 billion worth of infrastructure projects would boost steel demand.

But the rebound has since been curtailed by signs end-user demand for steel in China, the world's biggest consumer and producer, remains weak despite a recent spike in steel prices. "Inquiries are very limited. It looks like most mills are done with restocking ahead of the holidays," said an iron ore trader in Shanghai.

The Chinese usually restock raw materials ahead of long public holidays, including next week's National Day break, although many mills may have replenished enough at this point.

A Brazilian cargo of 65.14-percent grade iron ore was sold on Monday at $114.50 per tonne, down $2 from the previous sale of a similar grade, while a 63.6-percent grade Brazilian shipment was sold about a dollar lower at $105.10, traders said.

Iron ore stockpiles at major Chinese ports stood at 97.25 million tonnes at the end of last week SH-TOT-IRONINV, up half a percent from the week before, equivalent to about 1-1/2 months of China's imports.

The rebound in iron ore prices earlier this month had prodded some traders to snap up cargoes, hoping to recover from losses in the last two months following a market rout that sliced spot prices by more than a third. But some have remained cautious, with China's steel demand staying sluggish.

"We have not bought cargoes for two months now because we are not sure about the future of the steel market. We don't want to take the risk of buying a cargo that can't be easily sold these days," said a shipping manager for an iron ore trading firm in Shanghai.

"The risk of losing money is bigger than earning a profit," he said, adding his company still has around 200,000 tonnes of unsold stocks at ports.

Shanghai rebar futures rose half a percent to 3,562 yuan ($560) a tonne on Tuesday, gaining for a second day, while spot Tangshan billet prices rose by 60 yuan per tonne on Monday.

"The demand on the ground for steel hasn't really changed, it's still weak. Some traders chase prices higher only to find out that actual physical demand is not as good as they thought," said the Shanghai trader.