"I don't hold grudges and my door is always open to you," he told told a dozen defectors at a private meeting with his caucus, several who attended the session told Roll Call.
Dissident Republicans fell short in their bid to force a second vote on electing Boehner as House speaker for the 113th Congress that convened Thursday.
The 12 Republicans either didn't vote or voted for someone else during the public roll-call vote Thursday, just five shy of the number needed to force a second ballot and possible replacement of Boehner as speaker.
Boehner faced sharp criticism from within his caucus and conservatives outside Congress for his handling of the final "fiscal cliff" legislation -- which, among other things, raised rates for the wealthiest taxpayers -- and for canceling a vote on a Hurricane Sandy relief bill.
One dissenter. Rep. Walter Jones of North Carolina, told The Hill that re-elected Rep. Justin Amash of Michigan tried to orchestrate the anti-Boehner movement. Amash and Jones were among four Republicans kicked off their committees by GOP leaders after the November elections.
Amash at first would not say whether he led the anti-Boehner effort and later denied it.
"Independently, people were upset and they came together," he said.
Rep.Tim Huelskamp of Kansas, another GOP lawmaker removed from his committee assignment, said party leadership threatened to strip members of committee assignments and withhold financial support for their campaigns.
The Hill said Huelskamp refused to provide specific names and examples.
Majority Whip Kevin McCarthy of California, the party's chief vote-counter, denied the allegations, calling them "crazy."
"That's not true in any state or form at all," he told The Hill.