Many had wanted to avoid the chaos of the previous leadership race, which concluded only last month, where Liz Truss beat Rishi Sunak in a vote of party members despite her rival commanding more support from MPs.
Contenders had until 2pm today to hit the threshold of 100 nominations from Conservative colleagues.
Former chancellor Mr Sunak quickly hit the number, emerging as the frontrunner with the public support of about half the parliamentary party.
Ms Mordaunt appeared to be far behind with only 26 public backers this morning.
In a statement, Ms Mordaunt said: “Our Party is our membership. Whether we are elected representatives, activists, fundraisers or supporters.
“We all have a stake in who our leader is.
“These are unprecedented times.
Despite the compressed timetable for the leadership contest it is clear that colleagues feel we need certainty today.
“They have taken this decision in good faith for the good of the country.
“Members should know that this proposition has been fairly and thoroughly tested by the agreed 1922 process.
“As a result, we have now chosen our next Prime Minister. This decision is an historic one and shows, once again, the diversity and talent of our party.
“Rishi has my full support.
“I am proud of the campaign we ran and grateful to all those, across all sides of our party, who gave me their backing.
“We all owe it to the country, to each other and to Rishi to unite and work together for the good of the nation. There is much work to be done.”
