It comes amid reports the Prime Minister is set to ease some restrictions when he addresses the nation on Sunday to outline plans for the next stage of the lockdown.
However, Scotland’s First Minister Nicola Sturgeon said at her daily news briefing today there will be no lifting of lockdown until the scientific evidence shows the virus has been sufficiently suppressed, potentially opening the door for different measures being applied in England compared to Scotland.
Speaking on BBC Radio Scotland's Good Morning Scotland programme, Mr Blackford said that the Prime Minister must work for a political consensus.
From his home on Skye, the SNP MP said: "It's important that we do work together. This is an absolute crisis that we are in and it's about life and death.
"As I and the First Minister have said, this shouldn't be about politics - this should be about the scientific and medical advice.
"That's the way our democracy normally works. In a situation like this, when lives really are at stake, it is important that we do things in the correct manner.
"I'm extending that hand of friendship to the prime minister. All of us want to work with him, but he has to show respect to the devolved administrations."
Mr Blackford added that he doesn't want different parts of the UK pulling in different directions, but stressed that the Scottish Government's responsibility is to the people of Scotland.
"We know that the infection rate - the R rate - is slightly above in Scotland," he said.
"First and foremost, the public would expect us to look after the interests of the people that live here."
Mr Blackford, who represents Ross, Skye and Lochaber, also renewed his call for the Brexit transition period to be extended in the wake of the coronavirus crisis.
"Business can't take a second hit and all of us need to concentrate on the crisis that we face at the moment," he said.
"Let's park these discussions on Brexit, on the future relationship (with the EU), until we get through this."
Mr Blackford also warned about the dangers of "mixed messages" regarding lockdown advice coming from the UK and Scottish governments.
"We are still facing an enormous death toll and everything we do should be based on the scientific and medical advice," he said.
"It is devastating to see what is happening here on Skye and I don't want to see that being visited on any other community.
"What we should be focusing on are the health considerations for the public and the absolute desire to drive down the impact of this virus.
Asked if the public should be given "some leeway" after weeks of strict lockdown, Mr Blackford warned that doing so runs the risk of a second spike.
"If we allow an earlier removal of restrictions, all we are going to do is run the risk of that second spike and the impact on the health of individuals and the economy will actually be greater.
"There has to be discipline and an appreciation from the population of what we are doing and why."
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