The union has proved its worth during the coronavirus crisis “time and time again”, Boris Johnson has said.
The Prime Minister said there has been good co-operation across the UK during the pandemic despite “surface differences”.
During a Downing Street media briefing on Friday, he was asked about support for Scottish independence and whether he is “the biggest threat to the union”.
Recent opinion polls have shown support for independence in Scotland at above 50% and the SNP apparently on course for victory in the Scottish Parliament election next year.
It's quite right that there should be distinctive approaches in some aspects of the way we approach coronavirusBoris Johnson
Mr Johnson said: “When you look at what’s happened during this crisis, there has been very good and very close collaboration – despite the surface differences and the polemics that you refer to – there have been very good discussions across the UK between public health authorities, between the scientific and medical officers.
“Actually, the agenda that is being pursued by all parts of the UK beneath the surface has been very, very similar.”
He said the “strength of the union” has helped the response to coronavirus.
The armed forces have helped deliver tests across the country, while the “might of the UK Treasury” got the furlough scheme up and running, he said.
He continued: “I’m conscious that people will want to try to make divisions.
“It’s quite right that there should be distinctive approaches in some aspects of the way we approach coronavirus.
“But I have absolutely no doubt that the union has proved its worth during this crisis time and time again.
“The oldest, most successful political partnership in the world and we certainly don’t want to see it broken up.”
The SNP said the Prime Minister is “rattled” by public opinion in Scotland.
Kirsten Oswald, the party’s Westminster deputy leader, said: “The Tories are desperate to try and politicise the pandemic at every turn – but Boris Johnson’s comments show just how rattled he is by public opinion in Scotland.
“The SNP Government is getting on with the job of suppressing the virus and protecting public health.
“But the Tories’ suggestions that an independent Scotland wouldn’t have been able to take the financial action needed to protect jobs and the economy are laughable – countries around the world, many the same size or smaller than Scotland, have been able to take the steps required because they are independent.”
Another day yesterday with no deaths registered of people with confirmed #COVID 🙏— Nicola Sturgeon (@NicolaSturgeon) July 17, 2020
My thanks to everyone across 🏴 - our collective sacrifices have helped get this virus under control. Please keep it up. Letâs not drop our guard now. Remember FACTS #StaySafe https://t.co/W4SncXJMaH
Meanwhile, Scotland has seen a further 17 people test positive for coronavirus in the past 24 hours, according to Scottish Government figures.
The numbers from Friday also show there have been no new deaths involving someone with a positive Covid-19 test, meaning the death toll under this measurement remains unchanged from Thursday at 2,491.
A total of 18,401 people have now tested positive for the virus in Scotland.
There are 316 people in hospital with confirmed Covid-19. Of these patients, three are in intensive care.
Responding to the figures, First Minister Nicola Sturgeon tweeted: “Another day yesterday with no deaths registered of people with confirmed #COVID. My thanks to everyone across (Scotland) – our collective sacrifices have helped get this virus under control. Please keep it up. Let’s not drop our guard now.”