A terse statement issued by the Glasgow-based engineering firm, headed by chief executive Keith Cochrane, said there was no certainty it would make a new offer to revive the deal.
Weir also revealed new details on the structure of the all-share proposal it had put forward. Metso shareholders would have received the equivalent of 0.84 Weir shares for each Metso share held.
That valued the Finnish company at more than £3 billion and was a premium of about 14% to its share price before the deal became public knowledge. If accepted it would have left Weir shareholders with 63% of an enlarged entity with a stock market capitalisation in the region of £8.5 billion.
Weir said: "The proposal was structured to enable the shareholders of both Metso and Weir to share in the very significant value creation that would result from material cost synergies in addition to further revenue synergies expected to be generated through the combination.
"In keeping with the spirit of the merger proposal, Weir had proposed that the combined company would have a significant presence in, and a long-term commitment to, Finland as well as the UK and would be listed in both Finland and the UK with full index inclusion in both countries, alongside shared management and board responsibilities."
While Weir reiterated its feeling there was a "compelling strategic rationale" for the deal, it warned it could walk away rather than return with a sweetened offer.
It added: "The board of Weir believes that it has made an attractive merger proposal and there is no certainty that it will revise the terms of its proposal."
Weir's strong response came after Metso's board said it had considered the proposal and was not willing to enter into talks about it.
The Finnish business, which counts Finland's state investment company Solidium among its shareholders, said its board carefully evaluated the Weir proposal but came to "the unanimous conclusion that this proposal is not in the best interest of Metso shareholders".
It added: "The Metso Board remains extremely positive and confident in Metso's standalone growth and value creation prospects by pursuing its current strategy."
Weir's deal ran into trouble almost as soon as details emerged into the public domain at the start of this month, with Solidium stating it felt Metso should remain independent.
The tie-up would have helped Weir extend further into the crushing segment of the mining equipment industry, where Metso is a market leader. It would also have given Weir an additional layer of protection from bigger predators in the sector such as GE.
Weir is keen to expand its mining arm and Metso works in many of the same markets but produces different products.
Analysts feel the crowded mid-sized industrial sector is ripe for consolidation in order to provide a wider range, and a greater scale, of equipment and services to cost-conscious clients.
Separately, a note from RBC Capital Markets suggests Weir may upgrade its full year expectations on the back of continued strong oil and gas activity in North America.
Weir is due to update the market on first quarter trading early next month, and RBC said "Whilst we would not normally expect Weir to change its full year guidance [at quarter one], we see a higher chance than normal."
Shares in Weir closed down 4p, or 0.16%, at 2535p.