"We do believe the reports of his death are credible," assistant White House spokesman Eric Schultz said at a press conference on Wednesday.
He said US intelligence agencies are currently reviewing those reports and the circumstances in which the Taliban leader died.
According to Schultz, the US government is still not in a position to confirm when Mullah Omar died.
Also read: Mullah Omar dead: Pakistan lied yet again
Afghan President Ashraf Ghani tweeted earlier on Wednesday that his government, based on credible information, confirmed that Mullah Omar died in April 2013 in Pakistan.
The spokesman for Afghanistan's National Directorate of Security, Abdul Hassib Sediqi, told EFE that the death of the insurgent leader occurred in a Karachi hospital.
"Mullah Omar was sick and was hospitalised two years and four months ago in a hospital near the city of Karachi. He died in the hospital, but we don't know if he died from an illness or from some other cause," Sediqi said.
"We've had this information for two years, but now it's more reliable," added the spokesman, who announced that more information about the Taliban leader's death will be provided in the coming days.
Reports about the Mullah Omar's death have been multiplying over the past few months.
In April, the Taliban released on the Internet the first official biography of Mullah Omar, denying his death in an unusual way.
The Taliban have, however, remained silent since leaks about their leader's death began to seep out and still have not commented on the matter.
Confirmation of Omar's death comes amid a rapprochement between the Afghan government and the Taliban after more than 13 years of warfare.