It said this will be a final offer of 467p per share and would mean GKN shareholders would own 60 per cent of Melrose - up from 57 per cent, and receive £1.4bn in cash.
Shares in GKN were up nearly two per cent in early trading this morning.
The turnaround specialist said all recent attempts to engage in "constructive discussions" had been refused by the GKN board.
In a letter to GKN shareholders, Melrose's chairman Christopher Miller said:
On the one hand you can join us on a journey of value creation by investing in a UK listed manufacturing powerhouse worth over £10 bn today and receiving £1.4bn of cash.
On the other hand your board is attempting a hasty fire-sale of GKN businesses before they have been given a chance to reach their potential and with damaging consequences, we believe, for all stakeholders.
The deadline for acceptance is 1pm on Thursday 29 March.
GKN, which has been battling to see off Melrose's hostile bid, announced on Friday that it had reached an agreement to merge part of its business with US-based auto parts firm Dana for $6.1bn (£4.4bn).
Today, Melrose said the Dana transaction was "prejudicial to GKN's UK shareholders" and in its view, marked a bad deal for other stakeholders.
GKN responded to Melrose's latest offer saying its board is currently evaluating the proposal.
"Shareholders are advised not to sign any document which Melrose or its advisers send to them. GKN directors will do the same in respect of their own beneficial shareholdings," GKN said. "A further announcement will be made in due course."
In a letter to shareholders, GKN's chairman Mike Turner said Melrose's offer was "simply derisory".
Earlier this month, Melrose shareholders gave their backing to its prior £7.4bn hostile bid, with 98 per cent in favour of the acquisition.
The Melrose approach first became public in January, with engineer GKN saying it had rejected an unsolicited offer, instead unveiling a plan to split its business.
The FTSE 100 firm's board unanimously rejected a bid from Melrose received 8 January that valued the company at 405p per share, a 24 per cent premium on its 5 January closing price.
GKN then decided a combination of its Driveline branch with Dana could provide "greater shareholder value" than its original plan, and said it was exploring that along with the demerger prospect. That was compared to the Melrose offer, rejected by the board as "fundamentally undervaluing" the firm and its prospects.
MPs have written to the business secretary saying the proposed takeover of GKN by Melrose should be blocked, while the Pensions Regulator has also warned that the move could affect the firm's ability to fund its pension scheme.
|A timeline of the Melrose-GKN battle|