Scotland’s outgoing first minister, Alex Salmond, has called for all 16- and 17-year-olds to be allowed to vote in UK general elections, in the wake of last week’s Scottish referendum.

In his first statement to the Scottish parliament since last Thursday’s no vote, Salmond said he wanted to thank “every single campaigner and voter, whatever your view or whatever your vote”.

Rising to applause from across the Holyrood debating chamber, he said: “This has been the greatest democratic experience in Scotland’s history and has brought us great credit both nationally and internationally.” He said the referendum campaign had resulted in Scotland having the most politically engaged population in western Europe.

Salmond said there was now an “unanswerable case” for 16- and 17-year-olds to be given the vote in all UK elections, and he urged party leaders at Westminster to make the change in time for next May’s general election.

He said: “There is not a shred of evidence for arguing now 16- and 17-year-olds should not be allowed to vote. Their engagement in this debate, this great constitutional debate, was second to none. They proved themselves to be the serious, passionate and committed citizens we always believed they should be.

“Everyone in this chamber should be proud of this chamber’s decision to widen the franchise. There is an overwhelming, indeed an unanswerable, case for giving 16- and 17-year-olds the vote in all future elections in Scotland, indeed across the United Kingdom. All parties in this parliament I think should make a vow to urge Westminster to make this happen in time for next year’s general election.”

Salmond, who announced on Friday that he was standing down as first minister and leader of the Scottish National party, welcomed the appointment of Lord Smith of Kelvin to oversee the process of further devolution.

But he told the parliament: “We all have a responsibility to hold Westminster’s feet to the fire to ensure that the pledges are met”. He said there was a “special obligation” on the unionist parties to do so.

He added: “The true guardians of progress are the energised electorate of this nation, who will not brook or tolerate any equivocation or delay.”

Lord Smith visited the Scottish parliament earlier in the day to meet senior cross-party figures. He said: “My message today to the political parties is a simple one: Scotland expects you to now come together, work together and agree the detail of what those powers should be.

“Time is tight but this is not an exercise in thinking about what we could do – that has been done. It is about agreeing on what we will do.”

Salmond told the Holyrood chamber that an enhanced devolution settlement should pass three key tests: would the new powers aid prosperity and offer genuine job creation; would they build a society fairer; and would they give Scotland a stronger voice on the international stage.

He insisted that maintenance of the Barnett formula, as promised by the Westminster parties before the referendum, was essential until such time as Scotland had full control of its own resources, as was ensuring that a Scottish parliament was enshrined in legislation.

Referring to the crowds of loyalists who rampaged through Glasgow city centre on Friday night, in some cases assaulting yes supporters, he expressed his support for Police Scotland’s ongoing investigations into “those who indulged in pre-arranged thuggery against peaceful demonstrations”.

He said: “The full force of the law will be enabled and expected to make sure we eradicate such behaviour from Scottish life.”

Responding to Salmond’s remarks, the Scottish Labour leader, Johann Lamont, said it was now clear that the settled will of the Scottish people was to remain within the UK.

She told the chamber: “Much has been made by the yes side of the 1.6 million Scots who supported their case. It is an amazing achievement to get that many people in a country of this size to vote for any proposition. But we should recognise the achievement of the no side, which gained two million votes of support who believed we are stronger as part of the United Kingdom.”

Referring to Salmond, she said: “While he might not have got he result he was looking for, we can all agree that the United Kingdom is now the settled will of the Scottish people.”

The SNP announced that its membership had grown by more than 24,000, taking it to over 50,000 and making it the third largest party in the UK, with the Liberal Democrats standing at nearly 44,400 members.