The company was initially more equivocal about its attitude to Katona, who has already been filmed for its Christmas ads, saying only that she remains under contract though it thought she shouldn't have done the TV interview.
It also refused to comment on The Sun's report that its executives are poised to end the former Atomic Kitten's £250,000 deal after an email sent round its headquarters detailed some of the complaints made by customers.
However, it has now said it is working with Katona to make sure that she has a "clean bill of health and is able to continue fulfilling her duties as a mum and with Iceland".
"Kerry has been a successful face of Iceland advertising for the last three years. Having seen her appearance on 'This Morning', we are also concerned about Kerry's health and well being and are working closely with her to make sure she gets the best support from us that is possible.
"Kerry takes prescribed medication for her bi-polar disorder and it is currently our belief that Kerry's slurred speech was due to this."
It has previously said it had first-hand experience of Katona taking her medication at the wrong time, but that after a short period she had been fit to resume her work.
Katona's car crash TV moment came when she went on ITV1's 'This Morning' on Wednesday to promote her new MTV1 documentary 'Whole Again', which follows her as she spends £15,000 to regain the figure she had before giving birth to four children.
She slurred her words during the interview with Philip Schofield and Fern Britton prompting the presenters to enquire about her health.
The reality TV star said her slurred speech was due to prescription medication and accused Schofield of ambushing her live on air.
The Sun today claimed Iceland was about to drop her after customer complaints such as "I wonder how you can use her as a figurehead for your 'Mum's gone to Iceland' campaign" and "I won't shop at Iceland until she is gone."
It would be costly for Iceland to drop Katona now as she has already been shot for its Christmas campaign, created by the Tom Reddy Agency, and is under contract until April.
The agency is currently recording radio ads with Katona and Coleen Nolan and has already shot the Iceland idents for the next series of 'I'm a Celebrity...Get me Out of Here!', which will air next month.
Tom Reddy, managing director of the Tom Reddy Agency, said that Iceland will not drop Katona until research shows that she is no longer popular with its target audience.
Reddy said: "Iceland shoppers are still very loyal to her... [and see her as] one of their own".
Reddy also said that Katona is monitored very closely and that continuous image research is conducted.
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