Republic rejects Waste Management unsolicited bid

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.