First Quantum said Inmet's rejection did not include any compelling alternatives to its proposal and presented only "generic and rehearsed arguments."
The investor meetings will give Inmet shareholders a chance to speak to and hear from members of First Quantum's senior management team themselves.
"We hope you will be able join us at these events," First Quantum chairman and chief executive Philip Pascall wrote in a letter to shareholders, released Thursday.
Inmet owns 80 per cent of the Cobre Panama copper project through Minera Panama SA, with the remainder owned by Korea Panama Mining Corp.
In rejecting the offer, Inmet said the offer of $72 per share, half in cash and half in stock, undervalued the company and its Cobre Panama project.
The company pointed to the risk of swapping Inmet shares for those of First Quantum and the bidder's relative lack of experience building a mine the size of the project in Panama.
Inmet also said this week it was in talks regarding a range of alternatives as it formally rejected First Quantum's hostile takeover bid.
First Quantum said Thursday that Inmet should also open talks up with it.
"The Inmet Board has not heard from us about our business and about our plans for the combined entity, even though Inmet shareholders have been offered the opportunity to participate in our future success through ownership of First Quantum shares," Pascall wrote in his letter.
"This clearly limits the Inmet Board's ability to provide a sound and reliable recommendation to you on the merits of our offer."
First Quantum has said the combination of the two companies would create one of the world's fastest growing copper miners with the potential to produce more than 1.3 million tonnes of copper annually by 2018.
The bid by First Quantum follows the sale of its operations in the Democratic Republic of Congo to Kazakhstani miner Eurasian Natural Resources Corp. for $1.25 billion.
First Quantum had written off the value of the assets in 2010 after its operations in Congo were nationalized by the government of the mineral-rich central African country
First Quantum increased its offer last month to $72 per Inmet share or about $5.1 billion after an earlier bid of $4.9 billion was also rejected.
Inmet shares were down 27 cents at $70.50 in trading on the Toronto Stock Exchange on Thursday.