Finance Secretary Kate Forbes has written to Stephen Barclay, Chief Secretary of the Treasury, seeking temporary changes to funding arrangements.
These include the ability to borrow up to £500 million this year to deal with Covid-19 and flexibility to switch unused capital budget to other spending.
Ms Forbes said the crisis makes the need for a "robust" review of funding arrangements clear.
The letter was sent ahead of a meeting of finance ministers from administrations in Wales, Northern Ireland, Scotland and the UK Government on Friday.
Ms Forbes said: "To be clear, this request is not about permanently revising the existing framework.
"Rather, it is about providing enabling relatively minor flexibilities given the extraordinary pressures that the devolved governments are currently under, to ensure that our fiscal powers are commensurate with the risks we face.
"However, our fixed budget could respond more effectively with some relatively minor fiscal flexibilities.
"I cannot emphasise how critical these are to our ability to support recovery. "
The letter makes three key requests, including the ability to reallocate capital underspend on day-to-day spending.
It also asks for the ability to borrow up to £500 million, with repayment periods extended to a maximum of 10 years from five years.
There should also be more flexibility on drawing down reserve money, it says, with the limit increased to £220 million.
Due to increased spending to tackle Covid-19, the Scottish Government's overall budget for the 2020-21 financial year currently stands at more than £52 billion, up from an earlier estimate of £49.25 billion.
Ms Forbes' letter adds the Covid-19 crisis shows an upcoming review of funding arrangements should be "robust".
She said: "I would welcome a discussion with you in due course on how our governments can work together to deliver this robust review.
"I recognise that the UK Government will expect us to consider all options to use our budget as effectively as possible to respond to the cost pressures of Covid-19.
"We are fully committed to doing that, and indeed have already identified significant reprioritisation to support our response."
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