Mr Swinney said without urgent action, there was a risk the low oil price could lead to the premature decommissioning of North Sea assets.
This would therefore result in further job losses in the sector.
In a letter to Chancellor George Osbourne, the DFM has called for an internationally competitive tax regime to be created for the North Sea region.
In addition, he has outlined four key actions the UK Government can take:
• A substantial reduction in the headline rate of tax, with the primary objective of creating an internationally competitive tax regime in the North Sea.
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• Removal of fiscal barriers for exploration and enhanced oil recovery (EOR).
• Fiscal reforms to improve access to decommissioning tax relief and encourage late life asset transfers. This will reduce costs and help prevent premature cessation of production.
• Urgent consideration of additional non-fiscal support, such as government loan guarantees, to sustain investment in the sector.
Mr Swinney said: "The North Sea oil and gas industry is facing substantial challenges. The industry, unions, and the Oil and Gas Authority have all raised concerns about the loss of highly skilled workers, and confidence levels are now at their lowest since records began in 2009.
"The Scottish Government will continue to do all it can to support the sector. It is clear, however, that the UK Government must take urgent action to reduce the headline rate of tax at the March Budget. The fiscal regime must not be a barrier to investment and activity in the North Sea.
"I believe there is also a real risk that the low oil price could lead to critical infrastructure being decommissioned early. That is why I have called on the Chancellor to use his March Budget to improve access to decommissioning tax relief and encourage late life asset transfers.
"The UK Government must also consider all options available to facilitate new investment in the sector, including the potential for additional non-fiscal support, such as government loan guarantees."
(LM)
