The prime minister has rejected claims that Brexit will result in a Westminster power grab.
Speaking during a visit to Ayr, Theresa May stressed that leaving the EU will give the devolved governments more powers than they currently have.
Mrs May is touring the UK to mark a year to go until the date on which it will formally leave the EU.
The Scottish government accused Mrs May of being "dishonest" over Brexit and "letting everybody down".
Both it and the Welsh government have repeatedly claimed the UK government's Brexit proposals are a Westminster "power grab" as some powers returning from Brussels will go to Westminster in the first instance instead of Edinburgh or Cardiff.
But Mrs May said: "Let's be clear, there is no power grab, we are not taking back any of the powers that are currently devolved to the Scottish government.
"Indeed the Scottish government will be receiving more powers as a result of us leaving the European Union.
"What we're discussing with the Scottish government is how we can do that and ensure that we still maintain the ability for Scottish farmers, for Scottish businesses, to trade freely across the whole of the United Kingdom, just as we are negotiating the agreement to ensure they can continue to trade freely with the rest of the European Union."
The UK government recently proposed the "vast majority" of the 158 powers in devolved areas that are currently exercised by the EU would go straight to the devolved parliaments after Brexit, as it had initially stated.
But it would retain control in 24 areas, at least in the short term, until UK-wide frameworks are worked out.
The Scottish and Welsh governments say this would still in effect give Westminster a veto over some devolved responsibilities.
But Scotland's first minister, Nicola Sturgeon, sounded relatively optimistic that an agreement over the issue could be reached after a recent meeting with the prime minister.
Mrs May said her government was having "good discussions" with Scottish ministers on the issue, adding: "We have put forward proposals as to how this issue can be resolved."
She added: "But we want to ensure as we do that that people, businesses here in Scotland are able to continue to trade freely across the whole of the United Kingdom today, that's what we're talking to the Scottish government about.
"We want to ensure that in simple things like selling food across the whole of the United Kingdom, that there aren't any barriers put up to doing that as freely it can happen today."
The Conservative leader also hit back at claims from the Scottish government and others that Brexit would damage the economy, insisting there are "real opportunities for the United Kingdom when we leave the European Union".
She said: "I believe we can negotiate a good agreement which is tariff free and as frictionless trade as possible, so we maintain those markets in the EU, but also that we open up markets around the rest of the world.
"Brexit provides us with opportunities."
Mrs May said she wanted the four nations across the UK to "come together and really seize these opportunities for the future".
The prime minister's visit came as the Scottish government published a report which concluded that leaving the EU will have "huge implications" for the country.
Scotland's Brexit secretary, Michael Russell, insisted that "there is no pot of gold" that will come as a result of leaving the EU, despite claims to the contrary from Brexiteers.
Mr Russell said: "Far from things clarifying in the last 12 months we've got even more uncertainty.
"If you are EU citizen who is living here then you are unsure about what lies ahead, if you are somebody who is involved in farming or fishing you are unsure about what lies ahead, if you work in a university you are unsure about what lies ahead.
"The issue is people don't know what is happening and with six months left of negotiating time, there are huge issues to be addressed that are simply not being addressed.
"So I think you have to look at this government and see it is letting everybody down, but it is also talking often nonsense about Brexit."