Madonna's charity, Raising Malawi, claims to have built 10 schools serving more than 4800 children, but Kaembe told the BBC that in reality she had built "classrooms at existing schools".
Relations with the Government worsened when Madonna was reported to have been angered when she, her four children and her entourage were made to queue and check in with ordinary passengers at the Kamuzu International Airport on their departure from Malawi last week.
President Banda's office responded with an explosive statement accusing Madonna of making unreasonable demands "because she believes she is a music star turned benefactor who is doing Malawi good".
"Granted Madonna has adopted two children from Malawi," point number three reads of an excoriating 11-point statement attacking the singer. It goes on to say that "Madonna wants Malawi to be forever chained to the obligation of gratitude".
Claiming that Madonna had accused the President's sister Anjimle Oponyo of "pulling the strings against her" because the singer had not been "receiving the attention and the graces that she believes she deserved", the statement archly points out that other celebrities of "equally dazzling stature" - including Chuck Norris, Bono and footballers David James, Rio Ferdinand and Gary Neville - had all conducted themselves with more decorum on charitable trips to the country.
Madonna called the allegations "ridiculous".
"I'm saddened Malawi's President Joyce Banda has chosen to release lies about what we've accomplished, my intentions, how I personally conducted myself while visiting Malawi and other untruths," she said in a statement on Raising Malawi's website.
Trevor Neilson, whose Global Philanthropy Group manages Madonna's charitable work in Malawi, said that Banda appeared to be "using her office to pursue the financial interests of her sister".
Madge vs Malawi: Statements
Joyce Banda
"Kindness, as far as its ordinary meaning is concerned, is free and anonymous. If it can't be free and silent, it is not kindness; it is something else. Blackmail is the closest it becomes."
Madonna
"I came to Malawi seven years ago with honourable intentions. I returned earlier this month to view the new schools we built. I did not ever demand special treatment at the airport or elsewhere during my visit."
- Independent