Referring to abuse suffered by politicians, the work and pensions secretary, said: "It's worst of all if you are a coloured woman. I know that Diane Abbott gets a huge amount of abuse, and I think that's something we need to continue to call out."
The remarks immediately triggered a backlash, and Ms Abbott said the term was "outdated, offensive and revealing choice" in a response published on social media.
Picking up on the comments from Ms Rudd, who herself was revealing abusive messages she had received, the Labour MP Danielle Rowley said: "Amber Rudd undermining an important point about abuse by referring to Diane Abbott as a 'coloured woman' on BBC Radio 2. She clearly gets her language from the same bygone era as her abhorrent welfare policies."
But Ms Rudd quickly apologised, posting on her Twitter account minutes later: "Mortified at my clumsy language and sorry to [Diane Abbott]. My point stands: that no one should suffer abuse because of their race or gender."
Historically, the term "coloured" was associated with enforced racial segregation in the United States during the era of Jim Crow laws - with African Americans forced to use "coloured-only" public services.
Ms Rudd's comments on BBC Radio 2's Jeremy Vine show also came as female Conservative MPs - including Ms Rudd - detailed online abuse they had received ahead of International Women's Day on Friday.
The work and pensions secretary returned to cabinet in late 2018 with the welfare brief, after she was forced to resign as home secretary during the fallout from the Windrush scandal.
Her apology, however, was not the first from a cabinet minister on Thursday, as just hours earlier the Northern Ireland secretary Karen Bradley issued a statement saying she was "profoundly sorry" for suggesting killings by soldiers and police during The Troubles were "not crimes".
Ms Bradley described her inflammatory comments as "misguided and ill-judged", but has since faced calls to resign from her cabinet position by a raft of senior Irish and Northern Irish politicians.
“Yesterday I made comments regarding the actions of soldiers during the Troubles," she said. "I want to apologise. I am profoundly sorry for the offence and hurt that my words have caused. The language was wrong and even though this was not my intention, it was deeply insensitive to many of those who lost loved ones."
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