The Prime Minister has promised to bring the Withdrawal Agreement Bill to write her Brexit deal into law before the Commons in the first week of June.
Talks between Mrs May and Labour leader Jeremy Corbyn have so far failed to reach agreement on the Brexit process and the DUP continues to oppose the deal due to the inclusion of the Northern Ireland backstop.
Asked if she believed the Prime Minister will secure support to pass the deal at the June vote, Nicola Sturgeon said: “It doesn’t look to me as if she has any chance of getting it through because nothing has changed.
“She hasn’t made any progress in the last few weeks and it seems to me to be more about preserving her own party than doing what is right for the country.
“The SNP will vote against it because that would take Scotland out of the EU, out of the single market, out of the customs union and that’s not in Scotland’s interests.
“If you want to continue to send a message that Scotland’s place is at the heart of Europe, then voting SNP [at the EU Parliamentary election] and strengthening our hand in that is the way to do it.”
The SNP leader was speaking after meeting EU nationals working at Glasgow University and said she planned to use the European election next week to send the message that Scotland wants to stay in Europe.
She said: “The EU nationals, people who make a contribution to Scotland, who consider Scotland their home are being treated appallingly and being subjected to huge uncertainty for them and their families.
“My message to them is that they are welcome here, we want them to stay in Scotland and this is their home.
“We’re optimistic, we’re aiming to win these elections and we’re aiming to use these elections, hopefully with the support of people across Scotland, to send a very clear, simple and unequivocal message from Scotland, which is Scotland wants to stay at the heart of Europe, we don’t support Brexit and we want an end to the Westminster chaos that is doing so much damage.
“And the way to send that clear, unequivocal message is to vote SNP and then we send it loudly and clearly.”
EU nationals working at Glasgow University told the First Minister about their experience of Brexit so far, with senior lecturer Maria Economou, who moved from her native Greece to Scotland with her husband in 2014, saying it was “very worrying” and that her family had sought legal advice regarding their status.
Having applied for settled status, which incurred a £65 fee for adults until this was scrapped by the UK Government, she said: “It’s not the money, although that adds up as well, it’s how you are treated as a citizen.”
Tracey Aydogan, head of international and academic recruitment for the university, said leading researchers approached for roles have cited Brexit as a reason for not wanting to move their families.