Endeavour announced its offer, a 13% premium to Centamin's last closing price, earlier in the day, seeking to gain control of Centamin assets that include the Sukari mine and Cleopatra project in Egypt and exploration projects in West Africa.
The Toronto-listed firm, which owns four West African mines, said Centamin had rebuffed several attempts to engage in talks.
"The terms of the proposal provide comparatively greater benefit to Endeavour's shareholders, do not adequately reflect the contribution that Centamin would make to the merged entity," Centamin said.
Endeavour said it planned to offer 0.0846 of its own shares for each Centamin share, worth about 126.27 pence per share.
The combined entity would have produced 1.2 million ounces of gold in 2019 at an all-in sustainable cost - a key industry benchmark - of $875 per ounce, which would make it one of the world's largest and lowest cost miners, Endeavour said.
Centamin shares, which have underperformed Endeavour's over the last two years, were up 13.5% higher at 127.30 pence at 1550 GMT, on track for their biggest one-day jump since 2015 and signaling investors think the proposed bid could be increased.
Endeavour's shares fell 3%.
"My idea of fair value is a lot higher up, it probably starts with a 2," said Eric Moore, portfolio manager at Miton Group, the ninth biggest shareholder in Centamin with a stake of about 1.4%, according to Refinitiv Eikon data.
"It might be this is just an opening shot and we'll see how it evolves."
The gold industry has seen a flurry of deals over the past year as companies attempt to squeeze more value from operations after years of subdued activity and low returns.
Barrick Gold's purchase of Randgold was followed by the Newmont and Goldcorp tie-up, and, more recently, the $1 billion takeover of Continental Gold by Zijin Mining Group.
Mark Burridge, fund manager at Baker Steel Capital Managers which owns shares in Centamin and Endeavour, said the deal was compelling because it would create a larger and "more investible" entity.
Centamin has struggled shifting from open pit to underground at the Sukari mine and said in October it was looking for a new chief executive after its incumbent retired.
"We believe the Endeavour all share merger proposal for Centamin would provide the management and operational direction Centamin has lacked for the past two years," analysts at broker Peel Hunt said.
Endeavour said Sukari would also benefit from the fact that La Mancha - a private gold mining group chaired by Egyptian billionaire Naguib Sawiris - would become a key investor. The Sawiris family is Endeavour's top shareholder with a 30% stake.
"We believe in the strategic rationale for this proposal and are fully supportive," Sawiris said in a statement, urging Centamin's board to engage with Endeavour.
A top Centamin investor said Egyptian government approval would be key to sealing the deal.
Endeavour first showed interest in Centamin in 2018 with a proposal that was promptly rejected. It then sent a formal proposal last month, hoping to engage with Centamin's board.
The Canadian miner said on Tuesday Centamin's board had refused talks without a so-called standstill agreement, which could restrict Endeavour's options in pursuing a deal.
If Endeavour succeeds in its plans, its shareholders would own about 52.9% of the merged entity, while the rest would be held by Centamin shareholders.
By Muvija M and Zandi Shabalala