SNP Westminster leader Ian Blackford suggested the result had cemented its case for a second referendum on independence in the event of a no-deal Brexit.
"We stood on a mandate of asking the people of Scotland to reject Brexit - that we don't want to be taken out of the European Union against our will so, (it was) a very clear message for ourselves and indeed the other Remain parties in Scotland as well," he told BBC Breakfast.
"So, we've really rejected Brexit and in particular we've rejected a no-deal Brexit."
Blackford said that a situation that sees Scotland "dragged" out of Europe would mean Westminster "has to recognise that the Scottish National Party has a mandate for an independence referendum and we need to be able to secure our own future as a European nation".
Scottish First Minister Nicola Sturgeon says she has a smile on her face over the results so far in the European elections.
Speaking during a visit to Dublin on Monday morning, she said: "It was very strange to watch the election unfold from afar, I got so twitchy at not being at the count watching the votes pile up, I started to say I wanted to go and gatecrash an Irish count to get a sense of the occasion, but I was talked down from that.
"It's an absolutely fantastic result from my party's perspective, we didn't just win the election, we are polling 20-plus points ahead of our nearest rivals, it's astonishing, astonishing for any party, but our party has now been in government for 12 years, so as well as being a very clear anti-Brexit vote, I think it's an endorsement of our party's record in government.
"The highest vote share for any party in the UK, I think one of the highest vote share for any governing party anywhere in the European Union. I've got a smile on my face this morning.
"One of the other really astonishing things about the election in Scotland last night was the collapse of the Labour vote. When I was first in politics all those years ago, the joke in Scotland used to be you didn't count the Labour vote, you weighed it, and now Labour polled 9% of the vote in Scotland.
"The lesson of that in this election is that they paid a price for sitting on the fence on Brexit "My party has taken a consistently anti-Brexit position and I think that's fair to say that was vindicated in the election so far."
SNP Westminster leader Ian Blackford said Labour had "paid the price" for their "constructive ambiguity" as he hailed his party's "best-ever" European election result.
"We've been in power in Scotland now for 12 years and I think the fact that we've had our best-ever European election result and we went to the people of Scotland and said a vote for the SNP is a vote to stop Brexit.
"It's a vote to respect the result that we had in Scotland in the referendum in 2016 when 62% voted to remain," he told BBC Radio 4's Today programme.
"I think Labour have paid the price for the constructive ambiguity that has been much talked about - you cannot face two directions at the one time."
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