First Minister Nicola Sturgeon has said her proposals for protecting Scotland's place in Europe are a "serious and genuine attempt" to "unify the country around a clear plan".
The options outlined in the paper - Scotland's Place in Europe - represent a "significant compromise" on the part of the Scottish Government, she said.
The document proposes the UK should remain in the European single market and the customs union.
It also sets out how Scotland could remain in the single market without the rest of the UK and proposes a substantial transfer of new powers to Holyrood after the country leaves the EU.
Launching the paper at Bute House in Edinburgh, Ms Sturgeon said: "I hope and expect that the UK Government in considering these proposals will demonstrate the same flexibility and willingness to compromise."
The Scottish Government has proposed the UK as a whole should stay in the single market by remaining "a party to the European Economic Area Agreement" and staying in the customs union.
Ms Sturgeon said: "I accept that there is a mandate in England and Wales to take the UK out of the EU.
"However, I do not accept that there is a mandate to take any part of the UK out of the single market.
"It would make no economic sense whatsoever for the UK to leave the single market. It would be entirely democratically justifiable for the UK to remain within it.
"So, the Scottish Government will continue to argue - and build common cause with others of like mind - for continued UK membership of the single market.
"However, I reluctantly accept that as things stand - given the rhetoric of the Conservative government - that seems an unlikely outcome."
The "second strand" of the paper proposes ways in which Scotland could stay in the single market - through European Free Trade Association (EFTA) and the European Economic Area (EEA) - even if the rest of the UK chooses to leave.
Ms Sturgeon insisted this option does not prioritise membership of the EU single market over continued free trade across the UK.
"It would safeguard both," she said.
"Talk of a hard border for Scotland has always rung hollow from a UK Government that says no such hard border will be required between a post-Brexit UK and the Republic of Ireland, a continuing member of the EU," she said.
The paper sets out how free movement of goods, services and people would continue across the UK, even with Scotland in the single market and the rest of the UK not, Ms Sturgeon added.
Under this option, the Scottish Government has proposed the rest of the UK and Scotland should both stay in the customs union - allowing goods to move across EU borders without customs controls.
"If the UK opts to leave the customs union, then Scotland - in common with other EFTA EEA countries - would not be in the customs union either," Ms Sturgeon said.
"There will of course be disadvantages to Scottish businesses if we are not in the customs union - although those disadvantages would be minimised if Scotland remains in the single market.
"However, under this proposal the border between Scotland and England would not be an external EU customs border. What is in effect a customs union now between Scotland and the rest of the UK would continue."
She added: "There will be those who say a differentiated option for Scotland such as the one we propose would be too difficult to achieve - and as I have said, the paper does not underestimate the challenges."
A Downing Street spokesman said the British Government welcomed the Scottish paper and would "look closely" at it. It is expected to be discussed in detail when the UK Government and devolved administrations meet at the Joint Ministerial Committee in January.
But the spokesman made clear Theresa May is determined to deliver a UK-wide Brexit and did not believe there should be a second referendum on Scottish independence.
"The Government is committed to getting a deal on exiting the EU that works for all parts of the UK - which clearly includes Scotland - and works for the UK as a whole," said the spokesman.
"The best way for that to be achieved is for the Government and devolved administrations to work together."
Ms Sturgeon said there are already examples of different arrangements in operation within the EU and single market, adding the solution for Scotland "would be different in detail and scale to many of those arrangements, but not different in principle".
The UK Government already appears open to a "flexible Brexit" approach in relation to different sectors of the economy, such as the City, she added.
"It will also be necessary to take a flexible approach in relation to Northern Ireland and Gibraltar. There is no good reason why such flexibility should not also apply to Scotland."
Ms Sturgeon also said that whatever the outcome of the Brexit negotiations, the devolution settlement should be "fundamentally revised".
Powers returned from the EU which currently sit within Scottish Parliament responsibility - for example, fishing, the environment, justice and agriculture - should be handed over, she said.
Powers that are not currently devolved but which would enable Holyrood to protect key rights - for example, employment law and social protection, and "a broader range of powers to protect Scotland's interests and support a differentiated solution" - for example, power over immigration, should also be devolved, Ms Sturgeon argued.
The final strand of the paper deals with the powers of the Scottish Parliament.
It argues that, in light of the removal of rights and responsibilities provided by EU law, "Scotland's interests within the UK demand that the devolution settlement be fundamentally revised".
"There must be no Westminster power grab," Ms Sturgeon warned.
Concluding her speech, she said: "The proposals in this paper are detailed, serious and reasonable.
"They are designed to respect Scotland's voice and protect our interests whilst also acknowledging the position the UK finds itself in."
The First Minister said the overall proposals are aimed "first and foremost" at the UK Government, since the negotiations to be launched by the triggering of Article 50 will be between the UK and the EU.
Ms May told Ms Sturgeon on Monday she will look "very seriously" at the Scottish Government's proposals - a commitment welcomed by the First Minister.
"It is beyond any doubt that the Brexit vote - with its different outcomes in different parts of the UK - has raised fundamental questions, not just about our relationship with Europe but also about how political power is exercised across the UK," Ms Sturgeon said.
"So, to the Westminster government, I say this - your response to these proposals will tell us much, perhaps everything, about whether the UK is, in reality, the partnership of equals you claim it to be.
"To our European partners, I today reaffirm our belief in, and commitment to, the core values of solidarity, co-operation and democracy that underpin the European Union.
"And to the people of Scotland I pledge this: I will continue to do everything I can to protect your interests as we navigate the challenging times ahead."
Ms Sturgeon said she has not changed her position on Scottish independence "one iota".
The First Minister has said a second vote on the country's constitutional future is "highly likely" after the UK voted to leave the EU, but the majority of Scots voted to stay.
Asked on Tuesday whether she still believes another independence referendum is highly likely, she told reporters: "I haven't changed my view on that at all since I stood at this very podium on the morning of June 24.
"But I also said that morning that ... I would not only look at independence as a solution to this, that I would examine all options. That's what we've done painstakingly over the last six months.
"I've put forward today serious and reasonable proposals.
"I have asked for them to be considered, so I think it is only fair that I fulfil my side of the bargain and give the UK Government time to do that before I immediately start talking about what I'd do in the, at the moment, hypothetical scenario that they reject these proposals."