Carwyn Jones has said he wants to see more UK trade with the US while staying in Europe's customs union.
Before a visit to North America, the first minister said that he would "press the case for developing a free trade agreement between our countries".
However, speaking in Washington after his arrival, he added that trade deals should be handled at a European level.
His visit began as Labour leader Jeremy Corbyn said he now backed maintaining a customs union with the EU after Brexit.
The Conservatives said Labour's position was in "chaos" - claiming Mr Corbyn's comments undermined Mr Jones's trip.
The first minister wants the UK to remain part of Europe's customs union, something which would prevent it from striking trade agreements with other countries, such as the US.
North America is Wales' biggest export market after Europe. Official data shows the value of exports declined since 2012 but rose again to almost £2.5bn in 2016.
The Welsh Government said 270 US-owned companies employ almost 50,000 people here.
Before landing in Washington, Mr Jones said: "America is Wales' most important business partner and I want to build on the strong trade links that exist between our two countries as we leave the EU.
"While in the US, I want to gain a better understanding of the USA's position on future trading arrangements with the UK and will press the case for developing a free trade agreement between our countries.
"Exciting opportunities for trade with North America lie ahead," he said, adding that he wanted to reassure investors and visitors from the US that Wales remains an outward looking country."
But in a later interview in Washington with the BBC, Mr Jones said: "These things have to be done very, very carefully. I'd prefer to see it at a European and US level.
"I think there are great dangers if you have a free trade agreement that isn't the right one for your country."
The Welsh Government has called on the UK to retain "full and unfettered access" to the single market, prompting rival parties to claim Welsh Labour was at odds with Mr Corbyn's stance that the UK should leave both the single market and the customs union.
However, Mr Corbyn announced on Monday he now supported the idea of a permanent customs union with the EU after Brexit.
Welsh Conservative leader Andrew RT Davies said this would make a new trade deal with the US, as advocated by Mr Jones, "impossible".
"While Carwyn Jones is in America pressing the case for a trade deal between the US and UK, his boss back at home undermines his trip," he said.
"This is complete chaos from two key figures in the Labour Party and the confused policy goes to show how damaging Labour would be for our economy."
The first minister's trip follows a visit by Welsh Secretary Alun Cairns to meet US investors last week.
Mr Cairns said: "We can now look to new markets in North America, in the far east, in Australia and New Zealand and beyond.
"Therefore in the US they see the UK, and our outward-looking ambition, as a positive step in their portfolio, for their projects in order to export further on."
Plaid Cymru's Brexit spokesman Hywel Williams said he was glad the first minister was in the US trying to secure more trade, but expressed scepticism about what he might achieve.
"I'm just not sure that this is money well spent going over there - making the news but not much else," he said.
Plaid will push for the UK to remain in the EU's customs union after Brexit with a vote on the issue scheduled in the Welsh assembly on Wednesday.
The party accused Jeremy Corbyn of being "disingenuous" in suggesting the UK could keep its current trading arrangements without being a member of the existing customs union and single market.