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Weir Group has dropped its attempt to take over Metso Corporation after the Finnish engineering firm rebuffed a second approach.

Glasgow-based Weir said it submitted an improved bid on 20 May which valued Metso at about 4.5bn euros.

It represented a 34% premium to Metso's share price on 26 May - the day before the bid was rejected.

Metso argued that the offer undervalued the company and was not in the best interests of its shareholders.

In a statement, Weir said its all-share exchange offer meant Metso shareholders would have owned about 40% of the combined group.

It also argued that the combined company could have achieved annual cost savings across both Weir and Metso of at least £150m a year.

The statement added: "The board of Metso did not engage with Weir and on 27 May 2014 rejected the proposal, based on its belief that the market does not fully value the prospects of Metso and that the proposal significantly undervalues Metso.

"Weir believes it made a compelling proposal but remains financially disciplined and therefore does not intend to pursue this opportunity further at this time."

Weir confirmed at the beginning of April that it had proposed a possible merger with Metso but the offer was later rejected.

At the time, Weir said it continued to believe there was a "compelling strategic rationale" for a merger.

Both companies produce industrial pumps and valves for global oil, gas and mining operations.

A deal would have helped Weir expand further into the heavy mining equipment sector, in which Metso is a market leader.