The iconic news anchor was on "Meet the Press" Sunday with a group of panelists, who were discussing what it would take to unite the country at this point. The convo weirdly went from the U.S. standing up to Venezuelan dictator Nicolas Maduro to Brokaw offering his take on how the GOP is grappling with a rising Latinx electorate.

Brokaw said one of the issues that's affecting the GOP these days -- according to people who confide in him, apparently -- is that they're worried the U.S. is becoming flooded with Hispanic voters, who by and large register as Democrats.

Then the xenophobia ... Brokaw said conservative folks have expressed fear of having "brown grandbabies" due to interracial couples. He piggybacked on that sentiment with his own two cents ... saying the Hispanic community should "work harder" at assimilating in this country -- namely, by speaking English and making everyone else comfortable.

The backlash was swift on social media ... and Tom followed up later Sunday by saying he felt terrible if part of his comments offended anyone in "that proud culture," adding that he's worked hard to knock down false stereotypes over the course of his career.

He finished by reiterating his point about both sides needing to work to find common ground -- but a lot of people took his statement as a de facto non-apology.