Wood Group has rejected a second takeover bid in a week from Dubai-based rival Sidara.
The Middle Eastern firm hiked its initial offer 3% to 212p a share, from 205p a share (£1.4bn).
But the Aberdeen-headquartered group concluded the bid "fundamentally undervalued Wood and its future prospects".
Sidara's offer remains well below the 240p a share bid made last year by Apollo Global Management.
The full statement from Wood read: "On 8 May 2024, the board of Wood announced it had unanimously rejected an unsolicited, preliminary and conditional proposal from Dar Al-Handasah Consultants Shair and Partners Holdings Ltd ("Sidara"), regarding a possible cash offer to acquire the entire issued and to be issued ordinary share capital of Wood.
"On 14 May 2024 Sidara submitted a further proposal for a cash offer to the board, which proposed an offer price of 212p per Wood share, representing an increase of approximately 3% to the initial proposal.
"The board carefully considered the latest proposal, together with its financial advisers, and concluded that it continued to fundamentally undervalue Wood and its future prospects. Accordingly, the board unanimously rejected the latest proposal on 15 May 2024.
"There can be no certainty either that an offer will be made or as to the terms on which any offer might be made. Further announcements will be made as appropriate."
Sidara has until 5pm on June 5 to announce a firm intention to make an offer for Wood or walk away.
Who is Sidara?
The Lebanese-founded design and engineering business rebranded to its new name last year.
It's reported that it sold down a $1.4bn (£1.12bn) stake in Australian engineering services group Worley in April, to prepare to approach Wood.
The company, founded in 1956, generates about half of its $2.3bn (£1.84bn) revenue in the US and was believed to have been interested in Wood as a channel to grow that further through new oil and gas projects and renewable energy.
Around a quarter of Wood's revenue last year was accounted for in the US.