According to The Daily Telegraph, the National Cyber Security Centre (NCSC), which is part of the GCHQ, warned the party that the process was at risk and that ballots could be changed without better security.
Former chancellor Rishi Sunak and foreign secretary Liz Truss are competing in the leadership contest to succeed Boris Johnson as the next prime minister.
Some 160,000 ballots were due to be sent out on Monday to Conservative Party members, but they are now not expected to arrive until as late as 11 August.
The NCSC said it believed there was no specific threat from a hostile state and its concerns focused around the vulnerability of the voting process.
A Conservative spokesman said: “We have consulted with the NCSC throughout this process and have decided to enhance security around the ballot process. Eligible members will start receiving ballot packs this week.”
The Telegraph reported that members were originally going to be able to change their...