India-owned Sembawang Australia has stepped up its efforts to buy the construction business operated by MacMahon Holdings, offering $5 million more than a current takeover agreement.

MacMahon is looking to become a dedicated full service mining contractor, and has agreed to a $20 million deal to sell its construction business to major shareholder Leighton Holdings.

But Sembawang Australia - a wholly-owned subsidiary of engineering and construction group Punj Lloyd - has since lodged a rival offer for the construction business.

The offer was conditional on Sembawang being granted due diligence access from MacMahon, but that was denied because of the agreement in place with Leighton.

MacMahon said on Thursday Sembawang had increased its offer to buyout the construction business for $38 million, up from the $25 million it offered on January 2.

Alternatively, Sembawang has offered to replicate the terms of MacMahon's agreement with Leighton, but beat the offer price by $5 million.

MacMahon said its board would consider the new proposal.

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