NEW YORK (AP) _ Fieldcrest Cannon Inc., facing an unwanted takeover offer from a rival textile company, said Thursday it has agreed to sell its carpet and rug business to Mohawk Industries Inc. for about $140 million.

Management of Fieldcrest, the nation's largest towel maker, said the sale of virtually all of the division that makes carpets and rugs under the Karastan and Bigelow brand names will enable Fieldcrest to focus on its core bed and bath textile businesses.

The buyer, Mohawk, is one of the country's leading makers of broadloom carpet for residential and commercial markets.

Fieldcrest Chairman James M. Fitzgibbons said in a statement that the sale will give Fieldcrest greater financial flexibility and allow it to direct resources to its more profitable operations. Fieldcrest expects to receive $119 million in after-tax proceeds from the sale.

Fieldcrest's Carpet and Rug Division runs 10 manufacturing plants and had sales last year of $235.5 million. It makes woven and tufted rugs, including broadloom carpets, contemporary area rugs and oriental design rugs.

''The management of the carpet and rug division has done an excellent job repositioning Karastan Bigelow into a profitable business. However, for the business to continue growing, we feel that it is in the best interests of the division to align itself with a larger player who can commit the necessary resources to expanding the business,'' said Fitzgibbons.

Jack Riley, president of the division, said the divestiture has been under consideration for a number of years as it has been Fieldcrest's desire to place greather emphasis on its main businesses. When the division formally was put on the block in 1988, Fieldcrest didn't receive any acceptable offers, he said.

The announcement of the sale released here made no mention of the unsolicited $330 million takeover offer Fieldcrest Cannon received last week from Springs Industries.

Riley said he didn't think the sale was in any way related to the takeover attempt but he said he couldn't speak for the company because he hasn't been involved in the situation.

A spokesman at Fieldcrest's Eden, N.C. headquarters weren't available.

Robert Slough, a spokesman at Springs corporate offices in Fort Mill, S.C. declined to comment and wouldn't say whether the company would re-examine its offer in light of Fieldcrest's agreement with Mohawk.

Fieldcrest last week reacted coolly to Springs' overture but left open the possibility that the two textile companies might eventually unite.

A union of Fieldcrest and Springs would create a textile powerhouse, building on Springs' strength as the country's largest maker of textile home furnishings, particularly bedroom linens. Springs doesn't make towels; Fieldcrest is probably best known for its Cannon and other towel lines.

Springs, based in Fort Mill, S.C., had 1992 revenues of $2 billion, with two-thirds of its sales from its home furnishings business, and earned $44.5 million.

Fieldcrest had 1992 revenues of $1.2 billion - most from its towel business - and earned $15 million.