Charter has so far rejected two offers from Melrose, the most recent of which valued it at £1.4bn, as it believes Melrose undervalues its two businesses, welding firm ESAB and air and gas handling arm Howden.
But Melrose, led by chairman Christopher Miller (pictured) said it would need Charter to open its books for due diligence before it would increase its offer price further.
“Melrose does not consider that it would be appropriate to proceed without access to satisfactory diligence and will not do so,” it said in a statement.
“Melrose is willing to consider increasing its proposal to reflect any information that demonstrates that it has materially undervalued Charter and justifies such an increase.”
It added that it would consider raising its offer without diligence only if rivals sparked a bidding war.
Charter has issued three profit warnings since November as its businesses have struggled with fluctuating demand and a tough economic climate. It is due to announce its own turnaround strategy shortly and is fighting to stay independent.