Scotland’s economy faces losing up to £16bn a year as a result of leaving the EU, according to a Scottish government forecast.

The updated analysis warns that a hard Brexit, in which the UK falls back on World Trade Organisation rules, would cost Scotland up to £12.7bn and cause real household incomes to fall by 9.6%, or £2,263 per head.

In contrast, staying in the EU could result in the UK economy growing by 2.4% if integration of Europe’s single market in digital industries, energy and services intensified.

That growth would add about £3.6bn to Scotland’s economy, the report said, implying that overall, the decision to leave the EU would cost it £16bn – more than 10% of Scottish GDP.

The Scottish first minister, Nicola Sturgeon, said the report strengthened the case for the UK to keep single market membership, but added that her government’s preference was still to remain a full member of the EU.

Despite growing support for a second EU referendum, she said the greatest opportunity to prevent a hard Brexit came from the coalition of opposition parties and anti-Brexit Conservatives who backed continued single market membership.

That was “absolutely, manifestly, beyond any doubt the option which will do the least damage to our economy”, Sturgeon said.

She was scathing about repeated claims by Jeremy Corbyn, the Labour leader, that single market membership outside the EU was impossible. It was a “ridiculous position” for him to take, Sturgeon said, as “Norway stands as the living proof that this just can’t be the case”.

Despite Corbyn’s resistance to pressing for single market membership, for instance by joining the European Economic Area (EEA), of which Norway is a member, she said there was an increasingly powerful coalition at Westminster in favour of doing so.

She admitted she had not yet sought talks with Corbyn to press for a joint stand on Brexit and hinted that she felt the Labour leader was ideologically opposed to the EU. Even so, Sturgeon said: “I do believe there is a majority to be harnessed [in favour of] single market membership.”

The paper analysed the potential impact of three scenarios: EEA membership, a Canada-style free-trade agreement, and reverting to basic WTO rules. She said every option would involve a “hit to the economy”.

EEA membership would still involve a 2.7% reduction in GDP (£688 per head), a free-trade agreement would cut it by 6.1% (£1,610 per head), and WTO rules would slash GDP by 8.5% (£2,263 per head).

However, Sturgeon was much less forceful about the option she championed last year, that Scotland should have a differentiated trade deal with the EU after Brexit, preferably by remaining in the single market even if the rest of the UK did not.

She said that was still an option and her Brexit minister, Mike Russell, pointed at the putative deal for Northern Ireland, in which it would have close harmonisation with EU rules to protect cross-border trade with Ireland. Russell said differentiated deals for different parts of the UK were entirely possible.

However, authoritative opinion polling published by NatCen showed this was unpopular among Scottish voters, with 67% believing Scotland should have the same trade rules as the rest of the UK.