KABUL, Afghanistan — A new crop of senior American officials in Afghanistan has been racing to contain a dual crisis on the battlefield and in a potentially explosive election dispute. But it is a different American figure — the mercenary executive Erik D. Prince — who has been the talk of Kabul these days.

More than a year after first laying out his plan to President Trump to privatize the American war in Afghanistan with a cadre of contractors — and a private air force — Mr. Prince, the founder of the Blackwater security firm that became infamous for killing civilians in Iraq, has seemingly been everywhere.

And as he has made his sales pitch directly to a host of influential Afghans, he has frequently been introduced as an adviser to Mr. Trump himself.

Mr. Prince is pushing his plan at a particularly vulnerable time for the country. Afghan security forces are dying at a record number of 30 to 40 a day largely in a defensive posture against a Taliban that has gained territory. The government is beset by repeated political crises as parliamentary elections, delayed for three years, are scheduled for this month. Presidential elections are set for April.