(New throughout, adds background on Cutrale and Safra's rationale for offer)

Juice maker Cutrale and investment firm Safra Group said on Monday they offered to acquire U.S. company Chiquita Brands International Inc in a $610.5 million cash deal that rivaled an all-stock agreement with Irish tropical fruit company Fyffes Plc.

Chiquita is attempting to close a merger with Ireland-based Fyffes, which the two companies announced in March. The combined market value of Chiquita and Fyffes is currently close to $1 billion.

Cutrale and Safra, both based in Brazil, said they were offering $13 per share in cash to Chiquita shareholders, a 29 percent premium to Chiquita's closing price on Friday.

Shares of Chiquita rose more than 30 percent in response to the competing offer. They were trading at $13.30, above the offer price of $13, indicating that investors may expect a bidding war for the company.

Shares of Fyffes, meanwhile, fell more than 13 percent on Monday.

Cutrale and Safra said their proposal had been sent to Chiquita's board of directors and urged the company to enter negotiations that will lead to a definitive takeover agreement.

Cutrale and Safra said they hoped to have a response from Chiquita by Friday.

Timing for the new offer comes as Chiquita stabilizes its earnings and as a lawsuit accusing the company of funding a paramilitary group in South America was dismissed by a U.S. appeals court, according to a person familiar with the proposed deal. Shares of Chiquita have also fallen since the Fyffes deal was announced.

Under the deal with Fyffes, the new firm was expected to be listed in New York but domiciled in Ireland for tax purposes. Washington is trying to curb so-called inversions, in which U.S. corporations move their tax domiciles abroad to countries with a lower tax rate.

Spokesmen for Chiquita were not immediately available for comment. Fyffes declined to comment.

The $7 billion global banana market is controlled by Chiquita, Fresh Del Monte Produce Inc, Hawaii-founded Dole Food Company and Fyffes.

Cravath Swaine & Moore LLP is advising Cutrale and Safra. Safra is controlled by the Brazilian Joseph Safra family. (Reporting by Olivia Oran and Greg Roumeliotis in New York; additional reporting by Martinne Geller in London; Editing by Chizu Nomiyama, Tom Brown and David Gregorio)