On a visit to Chicago, planned to coincide with the Ryder Cup golf tournament, the First Minister said his country had fewer economic powers than Illinois.
But he claimed that an independent Scotland would be able to play a “full part on the world stage” and insisted relations with the US would “flourish” if Scotland broke away from the rest of the UK.
Mr Salmond also said the people best placed to make decisions about a country’s future where those who chose to live and work there.
He added: “They will always be the people who care most. That was true of the USA in the 18th century and today – it is also true of Scotland.
“Smaller independent nations are now benefiting from their natural economic strengths – flexibility, speed of decision-making and the ability to clearly define national interests and strategies. Scotland’s current constitutional status - as part of an incorporating union where one nation is always likely to prevail on the basis of its size – seems more and more like an anachronism.
“Scotland is still ranked number one in the world in terms of the impact of our life sciences research relative to GDP, and our researchers have a strong tradition of working collaboratively with industry.
“These economic strengths are supported in Scotland by a public sector which is absolutely committed to meeting business needs, and works together in a co-ordinated way to help companies. They help to explain why international businesses are coming to Scotland in ever increasing numbers.”
Mr Salmond, who was addressing the Chicago Council on Global Affairs, will be staying in the city until the end of the Ryder Cup to take part in the official handover ceremony on Sunday ahead of the staging of the event at Gleneagles in 2014 - just weeks ahead of the independence referendum.
He added: “Of course we will remain close friends of nations, such as the USA, with which we share such long-lasting ties of trade, family and friendship. The US will remain our biggest trading partner, biggest foreign investor and biggest tourism market outside of the current United Kingdom.
“With greater powers, we will do even more to improve the prosperity and well-being of our people. We will fulfil our duties as a good global citizen. And we will re-enter the community of nations on a basis of equality, responsibility and friendship.”