UPDATE 4-Terra Industries rejects sweeter bid from rival CF

* Terra calls CF offer inadequate and opportunistic

* Says offer not in best interests of its shareholders

* CF says offer "full, fair and compelling" (Adds new details, analyst comment, Agrium comment)

By Michael Erman and Euan Rocha

NEW YORK/TORONTO, Nov 4 (Reuters) - Fertilizer maker Terra Industries Inc (TRA.N) rejected a sweetened $4.1 billion takeover bid from rival CF Industries Holdings Inc (CF.N) on Wednesday in the latest twist in a takeover battle going on since January.

Terra, which has been fending off CF since January, called the latest bid inadequate and opportunistic.

CF on Sunday offered $32 in cash and 0.1034 of a share of CF common stock for each Terra share. The bid includes a special dividend of $7.50 a share that Terra plans to pay.

The bid valued Terra at $40.86 per share as of Wednesday morning. CF had previously made an all-stock bid of 0.465 CF shares for every Terra share, which would amount to $39.93 based on Wednesday stock prices.

Sioux City, Iowa-based Terra said the proposal continues to undervalue its near-term and long-term prospects.