The dispute over his views on trans rights, which has haunted his campaign from the outset, has also continued to show great distraction.
Nadine Dorries launched a new attack on hopeful leadership for her role in maternity legislation that referred to pregnant women rather than women.
The Secretary of Culture said Ms Mordaunt had sent her text message dismissing her concerns and told her to “not focus on this, but on the positive aspects”.
Ms Mordaunt has insisted she fought for the language to be changed, although that claim has also been answered by Attorney General Suella Braverman.
It launched an attempt to reclaim its bid for issue 10 on Tuesday with a commitment to give local residents more legal powers to block developments.
Writing in The Telegraph, he has pledged to strengthen neighborhood plans, which allow communities to choose where new homes are built.
“We need to build, but we can only do it with the support of communities, rather than leaving them harassed by developers,” he said.
Community involvement leads to “more construction”
“We know that communities involved in local plans end up supporting more construction, not less, because they feel empowered.”
Ms Mordaunt has also promised to rule out the binding house-building targets currently being imposed on town halls, arguing that they “don’t work”.
He said he would do more to protect the land from the green belt of development, but would also reduce bureaucracy, which is delaying work in thousands of abandoned sites.
Ms. Mordaunt added that she would place great emphasis on building more in urban areas to “invigorate and revive our city centers”.
On Monday, with a shocking result, Ms Mordaunt fell back to the third round of leadership voting, leaving one supporter but still came in second with the support of 82 MPs.