The announcement came only hours after AmeriTrade (search) said its board had decided the Omaha-based brokerage was not for sale.
It was not immediately clear how much E-Trade's offer was worth.
The company said its proposal would give AmeriTrade shareholders a 47.5 percent stake in the combined company plus about $1.5 billion in cash. It would also call for joint participation in senior management roles and representation on the board of the merged company.
E-Trade (search) forecasts that the transaction would result in at least $650 million in cost savings and added revenue.
E-Trade chief executive Mitchell H. Caplan would have led the company, E-Trade said.
In its earlier news release, AmeriTrade said it was confident in its own growth strategy.
"The board believes there will likely be further consolidation in the industry, but confirmed AmeriTrade is not for sale," founder and chairman Joe Ricketts said.
AmeriTrade shares rose 23 cents, or 1.67 percent, to $13.99 in midday trading on the Nasdaq Stock Market, where it has traded in a range of $9.75 to $14.61.
Analysts have said a desire to cut costs amid falling trading volumes could be driving merger attempts in the online brokerage industry.
AmeriTrade chief executive Joe Moglia said in the company's news release Thursday that AmeriTrade has been involved with seven merger and acquisition deals in the past four years.
"AmeriTrade is a leader in consolidating this industry," Moglia said. "We will continue to explore strategic opportunities, basing our decisions on whether a transaction will enhance shareholder value and benefit our clients."