May 28 (Reuters) -ICE cotton futures rose to an over one-month high on Tuesday, supported by a softer dollar and short covering from the investors.

* Cotton contracts for July CTc1 rose 0.93 cent, or 1.15%, at 81.45 cents per lb by 12:37 p.m. ET (1637 GMT).

* The dollar index fell 0.1%. A weaker dollar makes cotton less expensive for buyers holding other currencies. USD/

* "We see mixed trading happening with both short covering, which was the same as what we saw last week and potentially some new participants adding into the market with long positions," said Bailey Thomen, cotton risk management consultant at StoneX Group

* Last week, cotton futures posted their best week in nearly a year, helped by strong demand from top consumer China and firm export sales data from the U.S. Department of Agriculture (USDA). COT/N EXP/COT

* "The big factor that the market is monitoring is just the weather situation in the U.S. and worldwide," Thomen said.

* Tornado-spawning thunderstorms that swept the U.S. Southern Plains and Ozarks have killed at least 19 people as of Monday morning across four states and wrecked hundreds of buildings, with forecasters warning of more severe weather.

* Adding to upbeat sentiment, Chicago wheat futures jumped 3% on Tuesday to a new 10-month high before paring gains as the market reacted to reduced harvest projections and shifting rain forecasts for top exporter Russia. GRA/

* Elsewhere, India is likely to receive above-average monsoon rains this year, the weather office said on Monday. Nearly half of India's farmland depends on the June-September rains to grow a number of crops such as rice, corn, cotton, soybeans and sugar cane.

Reporting by Anushree Mukherjee in Bengaluru; Editing by Alan Barona