McCarthy, a five-term congressman from Democratic-leaning California and a frontrunner for the job, wrote a letter to fellow House Republicans yesterday seeking their support, after spending the weekend contacting every member of the caucus following Boehner's sudden resignation announcement on Friday.
The battle for the top congressional position comes amid intense party infighting, with the hard core conservative faction clashing bitterly with the Republican establishment.
His resignation announcement highlighted the precarious fissures within the party, as Republicans try to reclaim the White House in 2016 following eight years of the Obama presidency.
McCarthy, 50, struck a note of internal reconciliation in his letter.
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"We can't ignore the differences that exist, but we can and must heal the divisions in our conference with work, time and trust," McCarthy wrote colleagues.
"I am running to be your Speaker because I know that the people's House works best when the leadership you elect listens to members and respects the legislative process entrusted to committees," he wrote.
McCarthy already faces a challenge from congressman Daniel Webster, who said yesterday he wanted to "push down the pyramid of power" to create a a more "member-driven" process in Congress.