WASHINGTON — In one corner was Interior Secretary Ryan Zinke, a swaggering cowboy type who once rode to work on a horse named Tonto and has faced at least a dozen ethics investigations.

In the other was Representative Raúl M. Grijalva, an Arizona Democrat who has been accused of having ethical issues of his own — and who is itching to take on Mr. Zinke next year from his perch as the chairman of a committee on Capitol Hill.

Their tensions exploded on Friday into one of the more remarkable public feuds in recent Washington history — a brutal exchange that began with Mr. Grijalva calling on Mr. Zinke to resign, followed by Mr. Zinke calling Mr. Grijalva a drunkard who had used taxpayer “hush money” to cover up misbehavior, and Mr. Grijalva telling Mr. Zinke to, in effect, bring it on.

“It’s hard for him to think straight from the bottom of the bottle,” Mr. Zinke wrote on Twitter, in a message that left many in the Capitol slack-jawed. “This is coming from a man who used nearly $50,000 in tax dollars as hush money to cover up his drunken and hostile behavior. He should resign and pay back the taxpayer for the hush money and the tens of thousands of dollars he forced my department to spend investigating unfounded allegations.”