Burroughs Corp., the nation's third-largest computer company, yesterday announced that it would seek to acquire Sperry Corp. -- a takeover bid that would create the world's second-largest computer company.

Burroughs announced the takeover bid in a statement that noted that "Sperry has not responded to its proposal of May 5, 1986, to initiate merger negotiations."

Burroughs said it would proceed with a preliminary $2.3 billion cash offer today for approximately 58 percent of Sperry's common stock, confronting Sperry with a hostile takeover bid if it declines Burrough's offer.

On Monday, Burroughs proposed to merge with Sperry, the fifth-largest computer company, in a $4.2 billion offer of cash and securities that valued Sperry stock at $70 a share. Burroughs had sought to merge with Sperry nine months ago in a $65 a share transaction but was rebuffed.

In an interview Monday, Burroughs Chairman W. Michael Blumenthal declined to say whether Burroughs would proceed with a hostile takeover of Sperry if the company does not respond to the bid. Blumenthal said there is "no deadline" on the offer.

The new $2.3 billion offer calls for Burroughs to buy 33 million shares of Sperry common stock for $70 a share in cash. The tender offer expires June 5.

After the tender offer, Burroughs said it would acquire the rest of Sperry stock for a mixture of Burroughs debt and preferred stock also having a value of $70 a share, for a total that is close to the original $4.2 billion Burroughs offer.

Sperry, which did not comment on the original Burroughs proposal, had no response yesterday.

"We are aware of the Burroughs announcement, but we're not commenting," said a Sperry spokesman, who added that he was not aware of a Sperry board of directors meeting to consider the offers.

Blumenthal, who served as Treasury secretary in the Carter administration, argued Monday that the merger would be "procompetitive" in an industry dominated by IBM Corp. He added that "we have complementary strengths" in multinational markets.

Burroughs, which is based in Detroit, had sales of $5.0 billion last year, while Sperry, based in Blue Bell, Pa., had revenue approaching $5.7 billion. By contrast, IBM's annual revenue last year exceeded $50 billion.

Both companies are "mainframe" computer suppliers: they make large-scale computers most commonly found in the data-processing departments of large companies. According to an International Data Corp. estimate, IBM has a 70 percent share of the mainframe market.

A combined Sperry-Burroughs enterprise might be able to capture up to 15 percent of the mainframe market, said Blumenthal, and with more than $2 billion in defense and aerospace revenue, such a company would be the 16th-largest federal government contractor.