President Obama said Thursday that Donald Trump's idea for a "deportation force" to help expel immigrants in the U.S. illegally was not only impractical, but contrary to the character of the country.

"The notion that we’re going to deport 11, 12 million people from this country -- first of all, I have no idea where Mr. Trump thinks the money’s going to come from," Obama said in an interview with ABC News on Thursday, estimating it would cost billions of dollars.

But beyond that he warned such a program -- perhaps a revival of a controversial Eisenhower-era effort -- would diminish America's standing abroad.

"Imagine the images on the screen flashed around the world as we were dragging parents away from their children, and putting them in what, detention centers, and then systematically sending them out," Obama said. "Nobody thinks that that is realistic. But more importantly, that's not who we are as Americans."

The president has been eager to engage in the 2016 presidential contest, particularly on the issue of immigration. At a recent Congressional Hispanic Caucus Institute dinner he noted how far the GOP had come on the issue since his predecessor, George W. Bush, had warned against "exploiting the issue of immigration for political gain" as he tried but ultimately failed to pass major immigration reform.

Obama said in the ABC interview that there has always been an anti-immigrant strain in America, "ironically, from folks who themselves two generations back or even one generation back were immigrants," he noted.

"It's the job of leaders not to play into that sentiment," he said. "We don't want, I think, a president or any person in a position of leadership to play on those kinds of fears."