Tory MPs have voted for the two leadership candidates should go through to the run-off vote among party members.
Rishi Sunak won 137 votes and Liz Truss gained 113 votes to remain in the race after Penny Mordaunt who picked up 105 votes was eliminated on Wednesday.
Mr Sunak has been the frontrunner, with Ms Mordaunt and Ms Truss vying for the second spot in the final round..
Conservative Party members will vote over the summer, with a result to be announced on 5 September.
A YouGov survey of 725 party members on Monday and Tuesday suggested Mr Sunak would lose to either Ms Mordaunt or Ms Truss in a head-to-head.
The poll had Ms Mordaunt beating Mr Sunak by 51% to 37% and Ms Truss beating him by 54% to 35%.
The current size of the Tory party membership is not known for certain, but at the last leadership election in 2019 it was around 160,000, and is thought to have grown since.
The Conservative website says members can expect to receive their ballot papers between 1 to 5 August.
The deadline for voting – which can be done by post or online – is 17:00 BST on 2 September.