A fresh drive for Scottish independence will be launched by the SNP this summer as the party seeks to capitalise on its popularity and win over a significant portion of those who voted No in 2014, Nicola Sturgeon has announced.

In a speech to her party's spring conference in Glasgow, the First Minister dramatically reopened the issue of Scotland's future in the United Kingdom by promising to “embark on a new initiative to build support for independence” after the EU referendum in June.

The grassroots campaign will be aimed primarily at so-called “soft No voters” who were willing to be persuaded of the benefits of independence at the 2014 referendum but remained unconvinced by polling day, SNP sources told The Independent on Sunday. It is likely to feature a national tour by Ms Sturgeon, who remains extremely popular in Scotland.

The First Minister stressed that the drive would “not be an attempt to browbeat anyone” who is still staunchly in favour of the Union, but would instead take the form of a national conversation on the subject. The announcement earned her an immediate standing ovation from the 3,500 SNP supporters gathered in the main conference hall.

“I know that many across Scotland support the Union as strongly as we do independence – I respect that,” Ms Sturgeon said. “But I also know that many wanted to be persuaded in 2014, but ultimately didn't find our arguments compelling enough. So we will listen to what you have to say.

“We will hear your concerns and address your questions, and in the process, we will be prepared to challenge some of our own answers. And, patiently and respectfully, we will seek to convince you that independence really does offer the best future for Scotland.”

Describing independence as a “beautiful dream”, the First Minister added: “Our success will depend on the strength of our arguments and the clarity of our vision. It will mean convincing the people of this country that independence is right, not for yesterday's world, but for the complex, challenging and increasingly interdependent world that we live in today.”

The SNP's strategists believe they only need to convince around 15 per cent of wavering Scots to back independence to be confident of winning a second referendum, having secured 45 per cent of the national vote in 2014 from a much lower starting point. Recent opinion polls on the subject show that the country is still divided down the middle on the issue.

The new drive will be funded entirely by the SNP, to avoid accusations that the party is using Scottish taxpayers' money to bring about the break-up of the Union. Campaigning is unlikely to begin before July, so it does not interfere with the build up to May's Scottish Parliament election and the EU referendum in June.

The announcement will go some way to placating those SNP supporters who are keen for the party to push for a second referendum as soon as possible, but will also leave it open to criticism that it is obsessed with the issue of independence.

Scottish Conservative leader Ruth Davidson said the new campaign proved that the SNP “just isn't prepared to let this go”, while Scottish Labour said the economic case for leaving the Union was “dead” due to the collapse in the price of North Sea oil. “Most Scots don't want to go through another referendum,” a spokesman added.

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With less than two months until the Holyrood election – at which the SNP is expected to achieve a comfortably majority – Ms Sturgeon also used her speech to outline the detail of several policies. The most significant was a pledge to channel more money into schools through reforms to the council tax, in an attempt to close the so-called “attainment gap” between rich and poor pupils.

Around £100 million a year will be raised by making Scots who live in larger homes pay more in tax to local authorities, with this cash going “direct to head teachers”, she said. Over the lifetime of the next parliament £750m will be pumped into the Scottish Government's Attainment Fund, which will be extended to all parts of Scotland.