The latest offer came after a first set of concessions made in November failed to address the European Commission's competition concerns while opponents have criticized the second batch of proposals offered last week as only incremental adjustments.
The Commission has expressed concerns about the merged entity's more than 90 percent share of the exchange-listed futures market and possible barriers to new players.
In addition to the submitted remedy proposal, both companies expressed their commitment to maintain the current level of their published standard fees for their European derivatives contracts for a period of three years, the exchanges said in a statement on Tuesday.
They said the offer was made in a letter to EU Competition Commissioner Joaquin Almunia.
Almunia told a news conference earlier on Tuesday that a decision on the deal was possible by the end of January. The Commission is scheduled to decide by February 9 whether to approve the merger.
Separately, a person familiar with the matter said the exchanges would be meeting with European Commission officials on Wednesday in a so-called state of play meeting to get feedback on last week's concessions following a market test.
The exchanges face the risk of regulators blocking the merger if they are not convinced by the concessions. Due to the tight time constraints, it would be very difficult for the companies to offer more.
(Reporting by Foo Yun Chee; Editing by Greg Mahlich)