The SNP has urged the UK to include safe routes for those fleeing persecution and has called for an end to the Borders Bill, which the party claims could see many seeking asylum in Scotland criminalised and marginalised.
Asylum is reserved to the UK Parliament and is the responsibility of the Home Office.
However, a Scottish Government spokesperson said: “Scotland stands ready to offer refuge and sanctuary.”
The message comes as thousands of Ukrainians flee their home country following a full-scale invasion ordered by Russian president Vladimir Putin.
The US estimates five million people could be displaced, and Poland alone is preparing to receive up to one million refugees.
According to the Scottish Government, the UK Government has not made them aware of any plans for Ukraine specific-refugee resettlement.
A spokesperson for the Scottish Government said: “If a resettlement programme is announced, or Ukraine nationals are accepted as part of existing programmes, the Scottish Government will work to support our local authorities and services to enable them to offer places and support refugees arriving.”
The Home Office has offered an extension to visas for Ukrainians already in the UK, and has disapplied some rules to allow the family of UK nationals living in Ukraine to join them here.
However, while welcoming these steps, the SNP says the Home Office “must go much further”.
SNP shadow home secretary Stuart McDonald said: "I urge the UK Government to bring forward a serious humanitarian response plan, including safe legal routes to the UK.
“This must include much broader rights for Ukrainian nationals to join both British and Ukrainian family members who are already here in the UK, rather than expecting them to seek asylum in Poland, away from their families.
“And it must also make clear we are willing and prepared to take Ukrainian refugees here as part of the Global Resettlement Scheme, if that is advised by UNHCR [United Nations High Commissioner for Refugees] and requested by our European allies.”
The SNP has also called for the UK Government to “ditch its attack on the Refugee Convention” through its “toxic” Nationality and Borders Bill.
Under Clause 11 of the Bill, which was rejected by Holyrood, those who are forced to take “irregular journeys” are criminalised.
This would include some Ukrainians fleeing Russia’s invasion.
The Scottish Refugee Council has said this clause should be removed to ensure Ukrainian refugees can seek safety.
A joint letter from British charities has urged the UK Government to welcome Ukrainians fleeing the Russian invasion and rethink its “harmful” Borders Bill.
The letter has 53 signatories, including leaders from Save the Children and Amnesty International UK.
The Scottish Refugee Council has said the UK must take “immediate steps”, including lifting all visa requirements for Ukrainians to fly to the UK, as Ireland has just announced.
Gary Christie, head of policy at the Scottish Refugee Council, said: “We need to see an urgent internationally co-ordinated humanitarian response that matches the scale of the crisis in Ukraine and neighbouring countries. As European countries open their borders to those fleeing the conflict, so must we.”
Mr Christie added: “We have longed called for a sustained refugee resettlement system in the UK that plans for 10,000 refugees to be resettled each year to the UK.
"Without this, we have a government that is ill-prepared to match the scale of need.
“Last summer, we received an overwhelming number of incredibly generous offers of support from people across Scotland in response to the crisis in Afghanistan.
"We know that the people of Scotland will want to show the same compassionate welcome to people fleeing Ukraine.
"But we need a structured resettlement programme that properly funds local authorities and communities to be able to deal with emergency situations such as those being displaced from Ukraine."
The number of refugees being resettled in Scotland has already been impacted dramatically by Covid. Just 259 refugees were resettled north of the Border through the UK Government Resettlement Scheme during 2020 and 2021, with half of those coming in the first quarter of 2020.
Scottish Greens MSP Maggie Chapman called on home secretary Priti Patel to “immediately establish safe and legal routes for Ukrainians to travel directly to the UK to claim asylum”.
She said: “The home secretary should take inspiration from countries such as Ireland and Moldova and ensure that the UK is ready to welcome those fleeing conflict, especially those who may be most at risk under a Russian occupation, such as journalists and LGBT people."
Scottish social justice secretary Shona Robison wrote to the UK Government last month asking for four nations meetings to be re-established to tackle the housing of asylum seekers in Scotland.
Earlier this week, the leader of the Scottish Liberal Democrats Alex Cole-Hamilton called for the Scottish Government to review its New Scots refugee strategy, which commits to better access to essential services such as education, housing, health and employment.
Mr Cole-Hamilton said Nicola Sturgeon should review the strategy to ensure “mechanisms are in place to support people fleeting this conflict".
Talking about the review of the strategy, Mr Cole-Hamilton said: "That is especially urgent in the light of the scale of the Russian offensive against Ukraine, but also because six months on from the fall of Afghanistan hundreds of refugees are still stuck in temporary accommodation, which can be far from family and prevent them moving on with their lives.
"Scotland is a warm and welcoming country and like most Scots I want to see our Government step up to the plate to help as many as possible of those in need.
"Since 1989 Edinburgh and Kyiv have been twin cities. In their hour of need we need to give that relationship real meaning."
A UK Government spokesperson said: “Our priority remains supporting British Nationals who are resident in Ukraine and their dependents who want to leave the country.
"We are working around the clock to process visa applications and are processing many applications in a matter of hours.
“The main Visa Application Centre in Kyiv has closed following the Russian Invasion but our centre in Lviv remains open for family members of British Nationals resident in Ukraine, and we have surged staff to the centres in nearby countries, including Poland, Moldova, Romania and Hungary.
“Ukrainian nationals are able to apply for visas from these centres and we have announced concessions for Ukrainians currently in the UK, to extend or switch their visa.
“We are working with other European countries to ensure that responses to any migration issues are practical and in the best interests of the Ukrainian people.”