HANNOVER, Germany-- President Obama said Monday he believes the ongoing migrant and refugee crisis is not just a European problem, but a U.S. problem as well.

Speaking with "CBS This Morning" co-host Charlie Rose in Germany before meeting with European heads of state, the president also expressed concern about how the conversation surrounding the crisis is impacting European politics.

"What I've said to them is that this is not just a European problem. This is our problem too," Obama said.

"But more importantly, more strategically, is the strain it's putting on Europe's politics, the way that it advances far-right nationalism, the degree to which it is encouraging a break up of European unity, that in some cases is being exploited by somebody like Mr. Putin."

Pressed by Rose on if he believes Russia's President Vladimir Putin is aiming to divide Europe, Obama said that Putin has not always been keen to the idea of European unity.

"Mr. Putin has generally viewed NATO, EU, trans-Atlantic unity, as a threat to Russian power," he said.

"Now, I think he's mistaken about that. I've indicated to him that, in fact, a strong, unified Europe working with a strong, outward-looking Russia -- that's the right recipe. So far, he has not been entirely persuaded."

Watch more of the interview on CBSN, "CBS This Morning," and "Charlie Rose."