The stock deal between No. 2 Republic Services and No. 3 Allied Waste Industries was worth $6.07 billion at the time.
"Our proposal clearly offers a better and more certain value alternative to Republic stockholders than the recently announced Republic-Allied Waste transaction," said Waste Management Chief Executive David P. Steiner.
Republic said its board of directors will review the $34 per share offer from Waste Management and respond "in due course."
The per share offer represents a 22 percent premium to Fort Lauderdale, Fla.-based Republic Services closing stock price of $27.90 on Friday.
Republic Services had about 181.9 million shares outstanding as of April 25.
Looking ahead, Waste Management expects the deal, if completed, will boost its earnings in the first year and provide cost savings of at least $150 million.
Waste Management also said Monday it expects second-quarter earnings to beat Wall Street's expectations.
The company predicts a profit of 64 cents per share, or an adjusted profit of 61 to 62 cents per share. It predicts sales will rise 4 percent to $3.49 billion.
Analysts polled by Thomson Financial, on average, expect earnings of 58 cents per share on revenue of $3.42 billion.
The Houston-based company will announce second-quarter results on July 29.
Steiner told analysts in a conference call Monday that the company did not seek the deal with Republic.
"We did not go out looking for this deal and did not contemplate making an unsolicited offer for Republic, but when Republic was put into play as result of their agreement with Allied, we were presented with an opportunity we felt we could not ignore," he said.
Steiner said the move does not signal a return to a strategy of growth through acquisition.
"Once we close this transaction we will spend all of our time and efforts to ensure a smooth integration," he said. "We will not look to make any other significant acquisitions."
He said Waste Management is at a disadvantage because officials have not been provided the same information as given to Allied.
Goldman Sachs analyst David Feinberg said in a note to clients Monday that Waste Management's offer appears aimed at a clause within the Allied Waste-Republic Services merger agreement whereby management must consider "superior offers."
Feinberg expected the announcement to pressure Waste Management's shares, but said the company's positive second-quarter earnings outlook Monday gives him confidence in his "Conviction Buy" rating.
Shares of Waste Management fell $2.25, or 6.2 percent, to $34.36 in afternoon trade Monday. Republic Services' shares rose $3.77, or nearly 13.5 percent, to $31.67.
A spokesman for Allied Waste Industries in Phoenix, did not comment specifically on Waste Management's bid for Republic Services. In a statement, he said Republic's proposed $6.07 billion stock deal for Allied creates "significant long-term value for the shareholders of both companies."
If the deal ultimately goes through, Waste Management's share of the industry would rise to 30 percent from 24 percent now, said Stewart Scharf, an equity analyst at Standard & Poor's in New York.
Steiner said in an interview that Waste Management will divest assets if required to do so by the U.S. Department of Justice. Identifying which assets to divest would not occur until after Waste Management and Republic meet to discuss the deal, he said.
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AP Business Writer Samantha Bomkamp in New York contributed to this report.
