In a controversial message to a freelance journalist on the social networking site Twitter, Abbott wrote: "White people love playing 'divide and rule' we should not play their game."
The Hackney MP used a hashtag which spelt "tactics as old as colonialism."
When asked for a comment in response, Abbott told Huffington Post UK: "I'm going to have to get back to you on that."
She later wrote her tweet had been "taken out of context" and apologised for any offense caused.
Confronted about the comments by Sky News, Abbott walked away to take a phone call.
Conservative MP Nadhim Zahawi has called for Abbott to quit her front bench job as shadow public health minister, or for her to be sacked by Labour leader Ed Miliband.