Green ports are Scottish ministers' concept for enterprise areas which will offer tax and customs exemptions.
The UK Government is hoping to create seven free ports in England, the first of which is due to open by the end of the year.
Ivan McKee, Scottish Trade Minister has said his proposals are an "adaption" of the UK Government's policy, which will include environmental guarantees and protections for workers.
The Trade Minister has written to Steve Barclay, the Chief Secretary of the Treasury, saying seed capital for free ports and green ports should be equitable around the UK.
Mr McKee said: "I want to ensure that green ports - embedded within their communities - build on Scotland's reputation as a dynamic, outward-facing nation and become exemplars of inclusive growth, well-being and sustainability.
"Businesses in Scotland firmly believe that green ports should be supported with access to the same level of seed funding offered to freeports in England, and I agree.
"It is important the UK Government supports the development of these ports equitably across the UK, not least to demonstrate commitment to the economic development model we have agreed and are pursuing here in Scotland."
He continued: "With Scotland's landmass comprising one third of the entire British mainland, it would be fair and proportionate to accommodate the establishment of two green ports in Scotland.
"I have met a range of stakeholders and note their shared commitment to the importance of ensuring green ports fit within the Scottish context and of the need for there to be more than one."
A UK Treasury spokesman said: "From boosting investment to creating thousands of jobs, our free ports model will maintain high standards on workers' rights, benefiting communities right across the UK.
"We are looking forward to welcoming the benefits of free ports to Scotland."
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