The bid is pitched at 725p - well below the 750p per share 3i had been expected to bid.
Analysts said that, although the bid is higher than the 705p per share 3i was ready to offer in January, at this level there was little to choose between the 3i bid and proposals tabled by Electra chairman, Michael Stoddart, for winding up the trust last week.
Electra, whose investments include Derby County football club and the former Her Majesty's Stationery Office, is offering to buy back up to 40 per cent of its shares at a price of 786p per share. Electra shares rose by 3p to 713p yesterday, while 3i shares rose by 4p to 626p.
One analyst speculated last night: "I think that 3i is looking for an honourable way to withdraw."
Brian Larcombe, the 3i chief executive, insisted that the offer of pounds 320.7 in cash and 65 new 3i shares for every 100 Electra shares was a fair reflection of what Electra is worth.
He said that although the value of the bid was well below the price set for Electra's tender offer, it represents a small premium to what 3i believes is the true underlying value of the assets in the trust.
"Instead of having to wait the five years that Electra itself has said the restructuring might take, we are offering people some cash now and an investment in 3i, the market leader with a track record. The alternative is to remain a shareholder in a highly geared wind-up vehicle which is not going to be making investments," said Mr Larcombe.
No offer is being made for Electra Fleming, the 50:50-owned venture between the trust and the investment bank Robert Fleming, which manages the trust's assets.
Michael Stoddart, the chairman of the trust who has returned from New York where he had talks with potential US backers, immediately rejected the 3i bid as "plainly inadequate".
He said: "We as a board are totally conscious of shareholder value and we believe that our reconstruction proposals offer value. We have had indications that people want to talk to us. If a reasonable offer comes then we will look at it."