Mrs May has written to Donald Tusk, the President of the European Commission to officially request an extension to Article 50 until the end of June this year.
As it stands, the default position remains that the UK will leave the EU without a deal on April 12, although MPs have previously voted against this outcome.
Writing on Twitter in response to the news, First Minister Nicola Sturgeon said: “Instead of decisive action - requesting a long delay to allow the issue to go back to the people - Theresa May just proposes more short term-ism and a new cliff edge.”
The SNP has backed calls for a second referendum on Brexit, something the House of Commons has also voted against a number of times.
Mrs May’s preferred extension date is designed to avoid the UK having to participate in scheduled elections for the European Parliament, which she insists would be unacceptable.
An extension to Article 50, which previously mandated that the UK would officially leave the EU on March 29, will have to be approved by the remaining 27 EU states.
It is not yet known whether President Tusk will recommend they accept Mrs May’s request, although he previously mooted a ‘flexible’ extension of up to a year.
SNP Europe spokesman Stephen Gethins added: “More than three years on from the EU referendum and the Prime Minister’s approach is still dictated by can-kicking and chaos.
“Theresa May continues to ignore Scotland and her proposal to seek a further short extension to June 30 2019 - which the EU has already previously rejected - demonstrates beyond doubt she is putting the interests of her fractured Tory Party above all else.
“It is clear that with the UK Parliament unable to reach a consensus - coupled with everything we now know on the damaging impact Brexit will have on the UK economy, jobs and living standards - it must now be the priority that the issue is brought back to the people in a fresh second EU referendum, with the option to remain on the ballot paper.”