External Affairs Secretary Fiona Hyslop has insisted there is a "growing consensus" around the need for a differentiated immigration system north of the border.
The Scottish Government wants powers to set a tailored migration policy based on the "unique needs and circumstances of Scotland".
Concerns centre around the impact of the UK Government's target to cut net migration to the tens of thousands and the prospect of the end of freedom of movement of EU workers after Brexit.
Scottish Government analysis published earlier this month stated the net migration target could cost Scotland's economy up to £10 billion by 2040.
It suggested that even if migration was only reduced as a result of the end of freedom of movement from the EU, Scotland's economic growth would be £5 billion a year lower by the same year.
The paper government has set out options for Scottish migration system, including specific criteria to address skills shortages, a new migration body and powers to make it easier for migrants' family members, and those of UK citizens, to join them in Scotland.
Ms Hyslop said: "The Scottish Parliament and government must have the devolved powers it needs to address those challenges and with the urgency we require.
"We're not a lone voice here, a consensus has been growing for some time, with every major party now seeing the need for a differential approach to migration."
She continued: "We need to make sure that we can try and develop an evidence-based argument that brings the consensus from Scotland together to make sure that we can persuade the UK government of the need for this change."
However opposition parties insisted the focus should be on reforming the UK-wide system, rather than handing powers to Holyrood.
Conservative MSP Jackson Carlaw said there was much within Scottish ministers' analysis with which his party "wholeheartedly agrees".
However, he added: "The SNP do invest heavily in proposals that would remove all restrictions and devolve immigration to Holyrood.
"I don't believe that in this case it convinces."
Liberal Democrat leader Willie Rennie said: "It depresses me that every time we face a problem in this chamber, the SNP come forward with the answer that they need more powers for this Parliament.
"We need to lead the debate across the United Kingdom, to tackle the problem across the United Kingdom."
Meanwhile Labour's Claire Baker argued any additional powers coming to Scotland to deal with the issue "must be justified" and there "must be a demonstrated need" for this.
But she stated: "Crucially any changes must maintain the cohesion of a UK migration system, they must maintain free movement within the UK and be compatible with the UK system. This can not be about disrupting the UK migration system.
"This may sound challenging to achieve but I believe there is much we can do to tailor and make the current system more responsive to Scotland's needs without additional powers."