The former US President said the biggest challenge facing the world was to safeguard people's "special identity" while recognising that "what we have in common with others matters more".
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He told an audience in London the Scottish referendum was a classic case of the challenge.
Mr Clinton was giving a talk at an event organised by the centre-left Policy Network think-tank.
Addressing politicians, including Lord Mandelson and Shadow Business Minister Chuka Umunna, he said: "We've got to keep working for common ground all around the world.
"I think the 21st century will be decided by how we handle the identity crisis.
"How do we keep our special identity? You're going to see this, you've got the Scottish referendum here. Classic case.
"Can you be Scottish and British? How are the Egyptians going to deal with their var- ious identities and still be Egyptian?
"Can we find a way to appreciate what is separate and unique about us and still think that what we have in common with others matters more?"
He suggested the focus on identity politics in countries around the world was hampering efforts to forge more effective common bonds, adding: "You can't have 51/49, 52/48 debate about that every single year.
"This is the triumph of identity politics that is zero sum and its negative reference instead of a common vision."
Mr Clinton was speaking at the Royal Institution of Great Britain in London. The event was due to be a "conversation" with Tony Blair but the former PM pulled out when his father, Leo, became ill. He later died.
Mr Clinton's comments followed a similar message from his former secretary of state Madeleine Albright during a visit to Scotland earlier this month.
She argued that fragmentation in Europe was not helpful in efforts to work together with the US and noted: "In this day and age we all have to try to figure out how to work together – not so much separately."
She also said she agreed with views in a recent Washington Post editorial on Scottish independence suggesting a more divided Europe was less powerful on the world stage.
Mr Clinton closely identified with Labour after his time in office, famously introduc- ing himself as "Clinton, Bill, Arkansas CLP" when he addressed the party conference in 2002. He and Mr Blair shared the notion of a "third way" in politics.
His latest comments were welcomed by the party.
Shadow Scottish Secretary Margaret Curran MP said: "Bill Clinton is the latest addition to a growing list of progressive political leaders from around the world who can see that the best way to deal with the challenges we face is to bind together, not break apart."
The SNP said it "stood ready" to take part in the common ground Mr Clinton was calling for.
A spokesman said: "An independent Scotland will continue to work closely with our friends and allies in the UK, the US and around the globe – but in a modern, 21st-century partnership of equal nations. And as such we will be able to play a full part in that working for common ground which Mr Clinton calls for.
"Independence is about who is best placed to make decisions about Scotland's future – not about identity, and as such it is perfectly possible for people to feel British in a politically independent Scotland."