Melrose had raised its offer to £8.40 per share for Charter, which valued the company at £1.4bn.
Despite the offer being a 40 per cent premium to its Wednesday closing share price, Charter's board said it did not reflect the business' true value.
Charter also announced its new chief executive, Gareth Rhys Williams, who has been recruited to replace Mike Foster, who stepped down a week after issuing the June profit warning.
Charter's share price dropped by 25 per cent last month after it announced a profit warning in its 20 June trading statement.
While the price has recovered, the board still feels the market undervalues the company, whereas Charter believes it can turn around the performance of its two industrial businesses.
But Charter said it had engaged with Melrose over the offer.
“Having reviewed Melrose’s revised proposal and given Melrose’s advisers the opportunity to provide certain important clarifications, the board of Charter continues to believe that Melrose’s revised proposal is opportunistic and undervalues the Company and its prospects,” it said in a statement.
Charter also said it was preparing to present its own strategy for returning the two businesses – welding business ESAB and air and gas handling arm Howden – when it delivers its interim results.