Nasdaq OMX Group and IntercontinentalExchange Inc appealed directly to NYSE Euronext stockholders on Tuesday, asking them to press the Big Board's directors to sit down to talk about their joint bid.

The open letter to NYSE shareholders on Tuesday is the latest salvo in the effort by Nasdaq and ICE to win support for their takeover of the operator of the New York Stock Exchange, which Nasdaq says would reduce market fragmentation without boosting costs.

NYSE Euronext directors last Thursday rejected a sweetened takeover offer from Nasdaq and ICE, preferring to stick by their earlier agreement with Deutsche Boerse AG for a friendly takeover. NYSE directors have not met with the CEOs of ICE or Nasdaq, who say their proposal is superior both financially and strategically.

As NYSE Euronext stockholders, which would you choose -- engagement on a financially superior proposal, or a story about why an inferior transaction is really 'superior?' Nasdaq CEO Bob Greifeld and ICE CEO Jeffrey Sprecher said in the open letter.

Simply put, your Board is ignoring corporate governance best practices and the market reality of the situation.

A U.S. anti-trust review is already well under way, the letter said.

NYSE stockholders should call on their directors to meet with Nasdaq and ICE CEOs to address concerns and start mutual due diligence, they said. Such a meeting poses no downside risk and only upside for stockholders, they said.

NYSE Euronext, which runs stock and futures markets in the Unites States and across Europe, offered a few more nuggets on Tuesday to shareholders deciding which, if any, of the proposed deals will succeed.

Terms of the lower Deutsche Boerse offer could be sweetened to provide more value, but any changes are more likely to come closer to July, when NYSE Euronext shareholders vote on the proposal, a company spokesman said on Tuesday.

The spokesman confirmed that CEO Duncan Niederauer sees the Nasdaq/ICE bid as not serious and one meant just to spoil our proposal, as reported on the Wall Street Journal's website.

Niederauer also told the paper that Deutsche Boerse and NYSE Euronext decided to merge their various platforms into one global platform, once merged.

The battle for the parent of the iconic Big Board has turned to convincing shareholders and also regulators, who are expected to do a thorough antitrust review on both sides of the Atlantic.

To this end, Nasdaq earlier on Tuesday said it would cut fees for NYSE-listed companies if its bid succeeded.

Nasdaq would lower the maximum fee cap paid by NYSE-listed companies to $450,000, from $500,000 currently, resulting in immediate savings to many NYSE companies, it said in a letter filed with the Securities and Exchange Commission.

Nasdaq-listed companies would see their fees unchanged, it said in a separate letter.

NYSE directors say the Nasdaq deal would be too risky and would be less valuable in the long term.

NYSE shareholders vote on directors on Thursday.

(Reporting by Ann Saphir; additional reporting by Jonathan Spicer; Editing by Gerald E. McCormick, Tim Dobbyn, Gary Hill)