The parent company of the global convenience store chain 7-Eleven has rejected a near $39bn (£29.6bn) takeover offer from a Canadian rival, arguing it “grossly undervalues” the company.

Last month, Tokyo-based Seven & i revealed that it had received a bid from Alimentation Couche-Tard setting the scene for what could be Japan’s biggest ever foreign takeover.

7-Eleven has grown into one of the world’s largest convenience store businesses, with more than 84,000 stores across 19 countries, including 13,000 in the US and 22,000 in Japan.

On Friday, the Japanese group sent a letter to Couche-Tard saying that the proposal of a $14.86-a-share cash deal was “not in the best interest of … shareholders and other stakeholders”.

However, the company, which said that potential competition and regulatory risks were a significant concern, left the door open to accepting a higher offer.

“We are open to engaging in sincere discussions should you put forth a proposal that fully recognises our standalone intrinsic value,” said Stephen Dacus, the chair of Seven & i’s board, in the letter. “However, we do not believe … the proposal you have put forward provides a basis for us to engage in substantive discussions.”

Dacus, who also chairs a special committee set up to examine the bid, said that Couche-Tard’s offer was “opportunistically timed and grossly undervalues” 7-Eleven.

In addition, the company said that even if the offer were to be improved, it would still not “adequately acknowledge the multiple and significant challenges such a transaction would face from US competition law enforcement”.

Montreal-based Couche-Tard, which owns the rival Circle K convenience store chain in the US, is listed on the Toronto stock exchange and has more than 16,700 stores and petrol stations across 31 countries.

The offer was one of the first takeover attempts after the Japanese government softened rules last year, making it harder for boards to ignore unsolicited offers. Previous rules made it easier for chief executives and directors to block bids against the interest of shareholders.

At the company’s annual shareholders meeting on Thursday, Couche-Tard executives told investors that they remained “confident” in their “ability to finance and complete this combination” but also said they had “walked away from many more deals than we closed”.

There has been speculation that part of 7-Eleven’s defence may be to present the nationwide chain as an essential part of Japan’s disaster support infrastructure, in a country that experiences as many as 1,500 sizeable earthquakes a year.

In the letter on Friday, the Japanese group said that while Couche-Tard acknowledged “the crucial role that Seven & i plays in everyday life in Japan … this is clearly an area that would require further discussion should we reach that point”.