Updated from 8:55 a.m. EDT

Ameritrade

(AMTD) - Get Report

said Thursday that it will continue to explore strategic alternatives in the merger-happy online brokerage space, but does not currently consider itself for sale.

The company, which fielded an overture from rival

E*Trade

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(ET) - Get Report

, said it believes further industry consolidation is probable.

"We will continue to explore strategic opportunities, basing our decisions on whether a transaction will enhance shareholder value and benefit our clients," the company said in a statement. "The board believes there will likely be further consolidation in the industry, but confirmed Ameritrade is not for sale."

A few hours after Ameritrade's statement, E*Trade said it did make a proposal regarding a merger of the companies. E*Trade said the proposal outlined a structure that would give Ameritrade shareholders 47.5% of the combined company, plus about $1.5 billion in cash.

The upshot of Ameritrade's statement is less than clear-cut. Considering those terms, with tweaking the deal could probably be definable as something other than an acquisition.

Another complicating factor is the position of Ameritrade founder and 30%-owner Joe Ricketts, who is said to oppose an E*Trade transaction but could nevertheless be forced to accept it under terms of a 2002 agreement with the company's board.

Ameritrade was adding 5 cents to $13.81. E*Trade was up 3 cents to $12.41.