Oracle President Charles Phillips said in a letter on Tuesday to BEA's board that he believed his company's offer was generous at $17 per share, and there were no other offers above that price.
"Oracle has no interest in a long, drawn-out process to acquire BEA," Phillips wrote, urging the BEA board to let shareholders vote on the proposal.
Oracle said its officials might meet with Icahn and other BEA shareholders to discuss their bid.
So far Icahn has not embraced Oracle's offer. BEA's biggest shareholder and a vocal critic of the company's management has said he was pleased by Oracle's interest but that its price was too low.
The $17-per-share bid was a 21 percent premium to BEA's closing price the day before the proposal.
BEA shares dropped 3.2 percent to $17.99 on Tuesday. The stock had surged 38 percent on Oct. 12 to $18.82 on expectations Oracle's offer could lead to a bidding war as some analysts have predicted the software industry is ripe for a round of rapid consolidation over the next few months.
But word of an offer from a second company or even talks that could lead to one has not emerged.
Oracle, the world's biggest maker of database software, said that BEA has refused to hold talks on its offer.
Besides databases, Oracle also sells business management software and middleware, or programs that help connect various computer systems. BEA also sells middleware.
Linda Varoli, vice president of research with Wall Street Access, said Oracle's letter is a "negotiating tactic" to put pressure on BEA's board to reconsider the offer. She said she expects Oracle will make good on its threat to pull the bid if the company does not respond by Sunday.
"It may be over in the near term," she said.
Oracle's offer for BEA represents what would be its biggest acquisition since it bought Siebel Systems for about $6 billion in January 2006.