Mlenga Mvula, spokesman for Lilongwe high court, told the Agence France-Presse news agency: "The court is looking at the application now to determine whether Madonna can adopt these two children". He was not available Wednesday night to respond to Madonna's denial.
Explaining her decision to adopt children from Malawi, Madonna told Harper's Bazaar in 2013: "I decided that I had an embarrassment of riches and that there were too many children in the world without parents or families to love them".
The singer, 58, appeared before Justice Fiona Mwale along with security and a small entourage.
She previously adopted two children from the African country: David Banda in 2006 and Mercy James in 2009.
But the "Material Girl" singer insisted to People that "rumors of an adoption process are untrue".
She also has a daughter, Lourdes Maria Ciccone Leon, now 20, who she had with Carlos Leon.
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Madonna denied she had been seeking an adoption. Previous year saw her involved in a custody dispute over Rocco with ex-husband Guy Ritchie.
Madge founded the charity Raising Malawi to address the poverty and hardship endured by the country's orphans and vulnerable children.
The charity also provides scholarships to female students, and is now building the country's first paediatric intensive care unit at the Queen Elizabeth Central Hospital, in Blantyre.
It was Madonna's first visit in almost two years to Malawi, where she has at times been embroiled in controversy after her earlier adoptions.
"The... process requires the court to make a ruling on the adoption".
But Banda's successor, Peter Mutharika, has struck a more conciliatory tone, thanking the star on behalf of his government for "the passion Madonna has for this country".