Oct 29 (Reuters) -ICE cotton futures rebounded on Tuesday, after hitting their lowest level in more than a month in the prior session, buoyed by strength in the oil and grains markets.

* Cotton contract for December CTZ4 rose 0.62 cent, or 0.9%, to 70.98 cents per lb at 12:20 a.m. ET (1620 GMT). The contract hit its lowest since Sept. 16 in the previous session.

* "It's just a relief rally after being taken down yesterday," said Jack Scoville, vice president at Chicago-based Price Futures Group.

* "Chicago grain markets are generally trading a little bit higher as well. Now we're seeing some new buying show up and it's spreading to cotton as well as the grains and crude oil," Scoville said. He expects the cotton market to trade between 68 and 72 cents.

* In the grains market, Chicago soybean futures edged higher with bargain-buying supporting prices, although abundant supplies from the freshly harvested U.S. crop are likely to curb gains. Wheat and corn were also higher. GRA/

* Oil prices rose more than 1%, reversing some of the previous session's 6% drop. Higher oil prices make cotton-substitute polyester more expensive. O/R

* A weekly crop progress report from the United States Department of Agriculture on Monday showed 52% of the cotton crop was harvested in the country as of the week ended Oct. 27, compared with 44% a week ago.

* "Drier weather across much of the U.S. belt this week will favor cotton drydown and harvesting," weather forecaster Maxar said in a weekly note.

Reporting by Sherin Elizabeth Varghese in Bengaluru; Editing by Shilpi Majumdar