HARTFORD, Conn. (AP) - The trash talking has begun.

In a stinging letter Friday, garbage hauler Republic Services Inc. rejected an unsolicited $6.19 billion cash offer from larger rival Waste Management Inc., saying the proposal "seriously undervalues" its company.

Republic, the nation's third-largest waste collector, instead wants to stick with its own deal announced last month to buy No. 2 Allied Waste Industries Inc. The all-stock agreement was worth about $6.07 billion at the time.

"Republic is not for sale," James O'Connor, the company's chairman and CEO, wrote to David Steiner, CEO of Houston-based Waste Management, in a letter dated July 18.

The investment office that manages the assets of the Bill & Melinda Gates Foundation Trust also disagreed with the deal. BGI owns 15.6 percent of Republic and 2.3 percent of Waste Management.

The investment office also thinks the deal undervalues the target company, lacks strategic rationale, and believes the regulatory process will be arduous and risky.

And it says Republic's shareholders would be best served by the proposed purchase of Allied.

Republic's O'Connor said the company's board was aware of its fiduciary duties, and that Republic remains off the market because of its prior agreement to buy Allied.

Financial analyses presented to officials of Republic and Allied support a valuation "substantially above" $34 a share, he said. Waste Management's proposal was announced Monday.

Waste Management's offer on Monday represented a 22 percent premium to Republic's closing stock price of $27.90 on July 11.

But as Republic's shares have climbed on the news this week, that premium has shrunk to 5 percent, based on the company's afternoon trading price of about $32.49 on Friday.

"In your press commentary, you referred to the Waste Management proposal as 'opportunistic,'" O'Connor wrote in his letter. "We believe that your proposal is opportunistic for you and that it will deny Republic stockholders the opportunity provided by the merger between Republic and Allied." Republic is based in Fort Lauderdale, Fla.

Waste Management said in a statement that it is mulling its next step, hinting it might sweeten the deal.

"We are disappointed in the Republic Board of Directors' unwillingness to consider Waste Management's proposal," the company said, adding its offer "could reasonably be expected to lead to a superior proposal," it said.

Brian Butler, an analyst at FBR Capital Markets, said Republic's rejection of the Waste Management offer was expected.

"I think Waste Management knew it was not going to happen at $34," he said.

The choice for Republic to acquire Allied or be bought by Waste Management will come down to money, Butler said.

"I felt that Waste Management can get the deal done in the $38-40 range," he said. "Anything less than $37 you go with Allied Republic," he said.

Butler said Waste Management may want to buy Republic because, as it said, it could save $150 million a year in boosting its size and to improve its ownership of assets such as landfills.

Another possible reason is to block the Allied-Republic merger, Butler said.

"If you want to be more cynical, it keeps a near competitor from being created," he said.

O'Connor said Waste Management's proposal will not prompt Republic officials to change their strategy "and we are concerned that it may be an effort by our largest competitor to disrupt our plans."

As of June 20, the value of Republic's acquisition of Allied was worth $6.07 billion, based on its offer of 0.45 worth of Republic share for each Allied share held.

Outstanding shares of Allied totaled 432.5 million as of April 24, 2008.

Today, that deal is worth about $6.32 billion.

Allied said in a statement that the Waste Management proposal "does not constitute, and could not reasonably be expected to lead to, a transaction that is more favorable to Republic stockholders" than the agreement with Allied.

Waste Management reported revenue of $13.3 billion last year. Republic and Allied combined reported revenue of about $9 billion in 2007.

Shares of Republic fell 5 cents to end at $32.45 in Friday trading, while Waste Management fell 5 cents to $35.51. Allied shares rose 31 cents to close at $12.13.