Robert Greifeld added on Wednesday that he and partner IntercontinentalExchange could possibly put a “fully reflective” offer on the table if the Big Board parent reveals its detailed financial records to them.

Nasdaq this month joined ICE to bid for the New York Stock Exchange parent company, which earlier this year agreed to be acquired by Germany’s Deutsche Boerse AG for $9.8 billion.

Though NYSE’s board rejected the higher offer from Nasdaq and ICE, the pair sweetened the bid on Tuesday with a promise to pay NYSE Euronext $350 million if regulators block their takeover plan — a move meant to ease the board’s antitrust worries, and to draw them to the negotiating table.

“We are keenly aware that we were uninvited,” Greifeld told analysts and media on a conference call that was scheduled to discuss Nasdaq’s record quarterly profit.

“But that has the ability to change as we put things on the table that obviously are attractive to shareholders, (and that) will also be attractive to the NYSE board.”

Greifeld said he will continue to try to convince NYSE shareholders of the benefits of his unsolicited $11.1 billion bid, noting they are primarily concerned antitrust regulators will block it.

Nasdaq has given “reams of data” about the plan to the US Justice Department, the CEO said, adding he expects to have a “two-way dialogue” with them in about six weeks.

The DOJ would have to sign off on the deal to merge the top two US stock exchanges, creating a virtual monopoly in listing public companies.

“We have a scenario that takes us out into April 2012, and we are prepared to pursue a plan,” said Greifeld, a fierce competitor to NYSE counterpart Duncan Niederauer.

Greifeld said he is taking a friendly approach, hinting it would be in NYSE’s best interest to give Nasdaq and ICE access to its books: “Clearly diligence is an opportunity for NYSE shareholders to allow us to put on the table an offer that’s fully reflective of the knowledge available to us,” he said.

Nasdaq’s shares were up 0.2 percent at $27.44 on Wednesday morning. NYSE Euronext shares were up 1.7 percent at $39.36.

Meanwhile, the Nasdaq Stock Market parent showed few signs it was distracted from its bread-and-butter operations, as robust derivatives trading boosted earnings.

Excluding one-time items, the company’s per-share profit was a record 61 cents per share, matching the average analyst estimate as compiled by Thomson Reuters I/B/E/S.

“The takeover battle didn’t appear to impact them whatsoever, they had a record quarter,” said Richard Repetto, analyst at Sandler O’Neil. “Almost all revenue lines increased, and they continue to see pretty big jumps in their data centers.”

Revenue rose 15 percent to $415 million, better than the $409 million expected by analysts. Costs rose 12 percent from last year, offset by a 26 percent rise in trading-based revenue at the US-based, trans-Atlantic company.

While Nasdaq OMX hit a market share nadir of 19 percent in all US stock-trading, it logged a 31 percent rise in derivatives trading, helped by the market reaction to unrest in North Africa and Japan’s earthquake and tsunami.

When Greifeld unveiled the takeover plan on April 1, he said record earnings in the first quarter in part made the move possible. It was the second straight record in terms of earnings per share, helped by recent share repurchases.

Including all items, Nasdaq earned $104 million, or 57 cents per share in the first quarter, up 70 percent from $61 million, or 28 cents a share, a year ago.

Nasdaq’s debt stood at $2.3 billion at the end of the quarter.

Some analysts and shareholders worry the company would end up four-times leveraged if it succeeds in buying NYSE Euronext’s stock, options, and technology operations, threatening its investment grade rating. ICE would take the derivatives operations under the plan.