House Speaker John Boehner (R-Ohio) overcame a revolt from House conservatives seeking to unseat him from his leadership post. (Jonathan Ernst/Reuters)

Speaker John A. Boehner (R-Ohio) said Wednesday that House Republicans are in the midst of a "family conversation" in the wake of Tuesday's move by rogue conservatives to dislodge him from the top job, and he would not rule out further retribution against unruly members.

Addressing reporters after a meeting with rank-and-file Republicans in the Capitol basement, Boehner acknowledged stripping Florida Republican Reps. Daniel Webster and Rich Nugent of their membership on the House Rules Committee. Webster ran against Boehner for speaker, and Nugent voted for him.

"Because of some of the activities on the floor, two of our members weren't put back on the committee immediately. I have not had a chance to talk to them. I have not had a chance to talk to our members," Boehner told reporters.

The speaker would not rule out leveling more punishment against Republicans who opposed him. In all, 24 voted for another candidate for speaker, while one voted present.

"This morning, I told the members the same thing I'm saying here: We're going to have a family conversation, which we had this morning, about bringing our team together. And I expect those conversations for the next couple of days will continue and we'll come to a decision about how we go forward," he said.

The speaker also criticized President Obama for threatening to veto Republican-backed bills to construct the Keystone XL pipeline and alter the federal health-care law.

"The president essentially is telling the American people he doesn't care what they think," Boehner said.

At a news conference on Wednesday, Speaker of the House John Boehner addressed the shooting attack that left at least 12 dead at a satirical newspaper in Paris. (AP)

And the speaker condemned the deadly Wednesday attack on the Paris offices of a French satirical publication known for provocative content on Islam. The incident is a reminder "that we should be vigilant," he said.

Boehner also argued that Republicans can fight Obama's executive actions on immigration in the upcoming debate over funding the Department of Homeland Security without risking the country's safety. Funding expires at the end of next month.