Oct 10 (Reuters) -ICE cotton futures slipped more than 1% to a two-week low on Tuesday, pressured by muted demand outlook for the natural fiber and weakness in grains and oil markets.

* Cotton contract for December CTZ3 was down 1.58 cents, or 1.8%, at 85.38 cents per lb by 1:04 p.m. ET (1704 GMT).

* "China is leaning on buying the Australian crop, but if Australia gets into the El Nino trouble then they may have to come to the U.S.," said Keith Brown, principal at cotton broker Keith Brown and Co in Georgia.

* U.S. cotton prices are unlikely to gain much traction this year despite lesser output as trade tensions push key buyer China to rivals Brazil and Australia, analysts said.

* Oil prices fell more than $1 a barrel, continuing a slide that began earlier in the day with traders focused on demand levels but still cautious as they watched for potential supply disruptions amid military clashes between Israel and the Palestinian Islamist group Hamas.

* Lower oil prices make polyester, a cotton substitute, less expensive. O/R

* Market focus turns to the World Agricultural Supply and Demand Estimates (WASDE) report due on Thursday.

* "We're probably seeing some traders and hedgers position themselves ahead of the October WASDE and we are expecting a cut in the U.S. crop," Brown added.
* In the grain market, Chicago wheat dipped, corn eased and soybeans extended losses pressured by an advancing U.S. harvest and Brazilian export competition. GRA/
* Elsewhere, Brazil 2023/24 cotton (lint) output seen at 3.002 million tonnes vs 3.169 million tonnes in 2022/23, the government's crop agency Conab said in the first forecast report for the 2023/24 grain cycle.

Reporting by Sherin Elizabeth Varghese in Bengaluru; Editing by Shailesh Kuber