ICE cotton futures rose for the third straight session on Tuesday as demand picked up after a sharp decline in prices last week, while investors seek further clarity on the long-awaited trade agreement between the United States and China.

Cotton contracts for March gained 0.03 cent, or 0.46%, to 66.10 cents per lb by 02:05 p.m. EST.

It traded within a range of 65.42 and 66.14 cents per lb.

"We had little too much sell-off staring last week, we started to rally back this week," said Jon Marcus, president of Lakefront Futures and Options brokerage in Chicago, adding that people are awaiting for something to happen on the US-China trade front.

Last week, cotton prices posted their worst weekly fall in nearly two months, mainly driven by US-China trade tensions and fears of excess supply.

"Overall, demand is slightly increasing. Regardless of this (US-China trade talks) entire situation, it will end up being a demand situation," he added.

China's Vice Premier Liu He, US Trade representative Robert Lighthizer and US Treasury Secretary Steven Mnuchin discussed issues related to the phase one agreement on Tuesday, China's commerce ministry said.

Adding to the optimism surrounding a trade deal, US President Donald Trump said both countries are close to agreement on the first phase of a trade deal.

"The prospect for a US-China trade accord to be agreed to and officially signed this year is looking slim, and this could potentially make index funds lower their exposure to cotton during January's rebalancing period," Louis Rose, director of research and analytics at Tennessee-based Rose Commodity Group, said in a note.

Total futures market volume fell by 4,759 to 17,417 lots. Data showed total open interest gained 224 to 197,537 contracts in the previous session.

Certificated cotton stocks deliverable as of Nov. 26 totaled 78,124 480-lb bales, up from 75,029 in the previous session.