NEW YORK (The Deal) -- Pilgrim's Pride (PPC) on Tuesday sweetened its offer for Hillshire Brands (HSH) to $7.7 billion in cash, trumping a rival bid by Tyson Foods (TSN) in the battle to bring the maker of Jimmy Dean sausages to the table.

Greeley, Colo.-based Pilgrim's Pride said it latest offer is $55 per share in cash, $1.3 billion - or $10 per share - above its original unsolicited bid announced late last month. Tyson Foods joined the fray days later, offering $50 per share for Chicago-based Hillshire.

Pilgrim's Pride said its latest proposal is not subject to any financing conditions or contingencies. The company said even at the higher price it still believes the purchase makes sense for its shareholders, noting that it anticipates being able to extract upwards of $300 million in annual costs from the combination and to use the increased cash flow the deal would generate to quickly pay down acquisition debt.

WATCH: More market update videos on TheStreet TV | More videos from Brittany Umar

The fight for Hillshire is a battle of two of the world's largest protein producers. Tyson is the planet's second-largest meat processor behind Pilgrim's Pride majority owner JBS of Brazil. Another large producer, Shuanghui International Holdings-owned Smithfield Foods so far has been silent, as has smaller producers including Perdue Farms Inc. and Cargill Inc.

Hillshire, which has a separate $6.6 billion deal pending to acquire Pinnacle Foods (PF), in a statement said it intends to hold talks with both Pilgrim's Pride and Tyson. The company said it was not withdrawing or modifying its Pinnacle merger agreement. Both Pilgrim's Pride and Tyson had pushed for that deal to be scuttled.

Pilgrim's Pride said its latest offer is 49% above Hillshire's share price prior to that company announcing its Pinnacle deal. The significant premium, coupled with investor concern over the amount of debt Hillshire would have to take on if it is to buy Pinnacle and remain independent, could cause shareholders to advocate for a sale.

Pinnacle would likely be owed a $163 million termination fee should Hillshire not complete the purchase.

Shares of Hillshire opened Tuesday above $58 apiece, implying that Wall Street believes Tyson could return with its own improved offer. Processed food companies like Hillshire are of value to meat processors because popular finished product tends to have more secure margins than raw meat.