Former US president Bill Clinton and his family have expressed heartfelt sorrow over the death of Elif Yavuz in the Nairobi terrorist attack.

The Harvard-educated woman, who worked for the family's Clinton Foundation, was expecting a baby in just two weeks' time with her partner, Australian architect Ross Langdon.

The pair were among at least 62 people killed during in the terrifying rampage by Islamist militants at Nairobi's Westgate shopping mall, which appeared to be drawing to a close on Tuesday morning, Australian-time.

After a three-day siege, the Kenyan interior ministry said troops were "in control" of the shopping mall and all the hostages trapped by the gunmen were believed to have been freed.

Mr Clinton, his wife Hilary and their daughter Chelsea said in a statement that Ms Yavuz had devoted her life to helping others, "particularly people in developing countries suffering from malaria and HIV/AIDS".

"She had originally worked with our Health Access Initiative during her doctoral studies, and we were so pleased that she had recently rejoined us as a senior vaccines researcher based in Tanzania," the statement said.

The Clintons said Ms Yavuz , 33, was brilliant, dedicated and deeply admired by her colleagues.

"On behalf of the entire Clinton Foundation, we send our heartfelt condolences and prayers to Elif's family and her many friends throughout the world," the statement said.

Faculty and students at Harvard University's School of Public Health have also paid tribute to the Dutch-born Ms Yavuz, a recent doctural graduate who completed her dissertation research on malaria in eastern Africa.

Dr Julio Frenk, the dean of the faculty at Harvard School of Public Health [HSPH], sent a letter to staff and students remembering her as a passionate and committed person who was determined to make a difference in the world.

"As one of her colleagues here at HSPH said: 'Elif brought laugher and love wherever she went. She lightened the lives of her HSPH colleagues and of the children she lived with in Uganda during her thesis work'," Dr Frenk wrote.

"Elif committed her career and her life to helping those in need. Her compassion was an inspiration to everyone she touched at HSPH and the broader global community in which she lived and worked. She will be deeply missed by all who knew her.”

Mr Langdon, 32, was a founder of the prize-winning architecture firm Regional Associates, which has offices in Melbourne, London and Uganda, where he and his partner first met.

A committed conservationist, he led all the firm's projects in East Africa, was completing an HIV-AIDS clinic in Uganda - which he designed without charge - and was about to start on a $35 million museum telling the story of the earliest fossil record of walking humanoids in Kenya

In a statement, Regional Associates said: "We are deeply saddened by the tragic loss of our friend and colleague Ross Langdon and his partner Elif Yavuz.

"Profoundly talented and full of life, Ross enriched the lives of all those around him. Ross's leadership on projects throughout East Africa was inspirational, and he will be will be very, very sorely missed by us all. Our deepest condolences and thoughts are with Ross and Elif's families at this very difficult time."

A Kenyan government spokesman, Manoah Esipisu, said the three-day-long siege at the Westgate mall was close to being declared over.

He said special forces combing the building were no longer encountering any resistance.

"Our special forces are inside the building checking the rooms. We think that everyone, the hostages, have been evacuated, but we don't want to take any chances," Mr Esipisu said.

"The special forces call this sanitising. At the moment they have not met any resistance, but of course we are not ruling out the possibility that there are a couple of them hiding in a remote room or corner."

After a day of fierce gunfire, huge explosions and black smoke that billowed over the Kenyan capital, the vast centre was quiet 60 hours after the gunmen stormed the complex.

With AFP