The veteran member of the House Foreign Affairs Committee called for Napolitano's ouster in the wake of the attack on the Northwest Airlines flight on Christmas Day.
Earlier this year, some Republicans called on Napolitano to step down after her agency issued a report warning of the dangers of right wing "extremists."
Burton made his remarks on Twitter:
Napolitano came under fire after she said Sunday that "the system worked," noting the crew of Flight 253 "took appropriate action" to address the terrorist plot as it unfolded.
But her remarks were met with instant criticism, prompting the Homeland Security chief to clarify herself during a round of media appearances Monday morning.
The secretary then conceded on Monday that the system did not work.
“Our system did not work in this instance," Napolitano told "The Today Show." "I think the comment is being taken out of context."
Other Republicans, such as House intelligence committee ranking member Pete Hoekstra (R-Mich.), have criticized the handling of the attempted bombing, saying that the administration has not done enough to address terrorist threats on the United States.
The Obama administration and several congressional committees have said they will launch full investigations into the attack allegedly carried out by 23-year-old Nigerian Umar Abdul Farouk Adbulmutallab.White House Press Secretary Robert Gibbs over the weekend stressed that the attack should be a "nonpartisan issue."
The comments. Oh the comments. Look at this little gem:
"Janet looks and acts like she should be doing the dishes and cleaning up at home…not running the security of our country…please…this administration is such a joke."