Story highlights President Obama said he welcomed Republicans talking about income inequality "if it actually leads them to take different actions"

Potential 2016 Republican contenders have started mentioning the growing income gap and pushing the party to do the same

The President views the improving economy after a difficult recession as a potential cornerstone of his legacy

(CNN) President Barack Obama sought to reclaim some ownership over an issue that is suddenly a hot topic among top Republicans, telling an audience on Friday that he welcomes his rival party focusing on income inequality, but questioned whether it was anything more than talk.

"Now that their grand predictions of doom and gloom and death panels and Armageddon haven't come true. The sky hasn't fallen, chicken little is quiet," Obama said. "The new plan is to re-brand themselves as the party of the middle class. I am not making this up."

To laughs from the Democratic National Committee audience in Washington, D.C., Obama added: "I am encouraged they are speaking about middle class and about wages. But there is this old saying, you can't just talk the talk. ... You've got to walk the walk."

Income inequality and the growing gap between the richest and poorest Americans has become a primary issue in the 2016 election and many Republicans vying for the party's nomination have focused on the issue. The comments have not gone unnoticed by Democrats and the White House.

"We're facing right now a divided America when it comes to the economy," said Sen. Ted Cruz, R-Texas, after Obama's January address to the nation.

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