The First Minister said Scots could enjoy a "tapestry" of different identities. He added: "People are entitled to have as many layers of identity as they wish. A Scottish identity is perfectly valid.
"It does not necessarily have to have an independent country but it is best expressed through an independent country."
Mr Salmond was responding to former US President Bill Clinton, who last week questioned the drive for Scottish independence, in a speech critical of identity politics.
The First Minister was in conversation with Channel 4 News presenter Jon Snow at a packed event in Glasgow. The event was part of the Fraser of Allander lecture series, a three-way partnership between The Herald, Strathclyde University, and the International Network of Street Papers.
Mr Clinton had said the biggest challenge of the 21st century was for people to reconcile different identities while recognising that common endeavours "matter more".
Mr Salmond rejected claims that his comments were at odds with his goal of independence.
He said: "One of the most appealing features of Scotland at its best is that Scottish identity is a non-exclusive identity.
"I've lots in common with Bill Clinton. There's nothing small minded or negative about having a Scottish identity, a European identity, an international identity. That's a perfectly valid, open minded way of looking at the world.
"There's nothing invalid about having an English identity, a European identity and international identity.
"For Bill Clinton there's nothing invalid about having an American identity and international identity.
"There's nothing wrong with feeling British either. We've got people in this city who have an Irish identity and Scottish identity, or a Kashmiri or Pakistani identity and a Scottish identity, people with an English identity and a Scottish identity.
"One of the most likeable features about Scotland at its best, and we're not always at our best, is that a Scottish identity is a non-exclusive identity."
He added: "The idea that you have to choose your identity, an English or British identity to the exclusion of other identities, it doesn't work like that in the modern world.
"I'm arguing that a Scottish identity is a perfectly valid identity to have, there's nothing small minded or to be ashamed about.
"It doesn't necessarily need to have an independent country, but I think it is best expressed through an independent country because people's identity and feelings are often expressed through the field of politics."
Mr Salmond welcomed support for the SNP from Asian Scots in the 2011 election and added: "That strikes me as an indication we are not going to ask people to choose between identities.People have a complex, fascinating tapestry of identities, a tartan of identities."
In a wide-ranging discussion at Strathclyde University's Barony Hall, the First Minister also defended SNP claims that an independent Scotland would automatically remain a member of the EU.
He claimed the Edinburgh Agreement, signed with the UK government to allow the referendum, confirmed that Scotland would not be seceding from the UK if Scots voted Yes, but that the UK would be dissolved, leaving both parts with the same, ongoing relationship with the EU.
Mr Salmond dismissed claims by the Institute for Financial Studies think tank which warned an independent Scotland would face tougher spending decisions than the rest of the UK as North Sea oil reserves ran down in coming decades.
He said: "The argument that oil is running out or of low value I think is nonsensical."
But emphasising the twin importance of renewable energy to Scotland's future, he added: "Donald Trump is establishing a very good golf course but he is not having much success dictating Scottish energy policy."
In a lighthearted moment at the end of the evening, after noting that both he and the First Minister had been boy sopranos, Mr Snow broke into song with The Wings of a Dove. Mr Salmond did not attempt to upstage him.
Mr Snow is an ambassador for the INSP, which represents 120 street papers worldwide, including the Big Issue.
The second conversation in the series will be between Alistair Darling, leader of the Better Together campaign, and Herald and Sunday Herald writer Alan Taylor on December 6. To book, visit the university's online shop at onlineshop.strath.ac.uk