He spoke to reporters in Montgomery at a news conference called to discuss budgetary issues with the state's Medicaid agency. He also spoke about prisons.
Before opening the floor, Bentley effectively pre-empted any questions about the scandal.
"I'm telling you right now do not ask me anything other than those two things," he said, referring to Medicaid and the state's prison system. "This state has some real problems and we're here to try to solve those problems."
This comes after a bipartisan group of Alabama lawmakers said they intend to introduce articles of impeachment against him.
"We're looking at this governor who has essentially betrayed the trust of the people of Alabama through actions and lies that have caused us to have some doubt about his leadership," state Rep. Ed Henry told reporters Tuesday.
"There is a crisis of confidence," said State Rep. Mike Ball, chairman of the House Ethics Committee. "And it needs to be resolved."
Henry and Ball, like Bentley, are Republicans, underscoring the uphill battle the second-term governor faces in the midst of a highly publicized sex scandal.
But Bentley has showed no signs of backing down.
"There are no grounds for impeachment, and I will vigorously defend myself and my administration from this political attack," he said Tuesday in a statement. "Today's press conference is nothing more than political grandstanding intended to grab headlines and take the focus away from the important issues the Legislature still has to address before the end of the session."
Audio recordings from 2014 surfaced last month of a sexually explicit conversation reportedly between Bentley and one of his former aides,
Rebekah Mason. Only the governor's voice is heard on the recording.
The governor didn't deny the authenticity of the recording when questioned about it.
Both Bentley and Mason have denied having a physical affair. Bentley and his wife divorced last year.
Bentley has apologized and maintains he did nothing illegal. He has said several times he won't resign.
The proposed articles of impeachment list four reasons why the governor could be impeached: Willful neglect of duty, corruption in office, incompetency, and offenses of moral turpitude.
"Impeachment is a serious thing," Ball said. "Impeachment is about undoing an election of the people."
How impeachment works
, articles of impeachment must be brought forward by the state House of Representatives, while the state Senate acts as jury. Most states follow a similar procedure, according to the National Conference of State Legislatures.
Henry, lead sponsor of the measure, said that while he has the 53 votes needed to move the bill up to the Senate for an impeachment trial, it was going to take some time.
"We have the votes to pass it," he said Tuesday. "But if we brought it up today, I believe it would fail."
That's because circumventing normal legislative processes -- such as committee assignments and hearings -- would require four-fifths of the House to vote in favor of suspending the rules.
"It's not going to happen today," Henry said Tuesday. "The process starts today."
Henry said he was pushing impeachment because the state House needs to be responsive to voters and not wait for the court system and law enforcement agencies to finish their work in the case.
"That would be passing the buck," Henry said.
Still, others are urging caution.
"We need to make sure that we gather the facts," said State Rep. Juandalynn Givan, a Democrat.
"If we're going to impeach someone for having an affair, many of the governors, legislators, and many elected officials throughout this country would not have the positions that they have," she said.
An apology at a prison
During a visit to a prison Monday, Bentley took some time to issue another apology.
"I've asked God to forgive me, but I've asked other people to again forgive me," he said. "I have truly asked the people of this state, that are the most loving and the best people in the world, I have asked them to forgive me."
The back story
Whether or not Bentley had an affair, many Alabamians are angry about what appears to be subterfuge coming from a politician who campaigned as an honest, principled conservative.
Spencer Collier, the former head of the Alabama Law Enforcement Agency, was fired on March 22
. After being ousted, Collier said he had seen text messages and heard audio recordings of "a sexual nature" between Bentley and Mason, the aide.
The tapes were made public by the Bentley family, according to AL.com, which published excerpts
. AL.com reported that it was allowed to hear portions of the tapes by people close to the Bentley family.
AL.com says the tapes were made by family members as they tried to figure out whether the governor was having an affair.
On one tape, Bentley could be heard saying: "When I stand behind you, and I put my arms around you, and I put my hands on your breasts, and I put my hands [unintelligible] and just pull you real close. I love that, too."
Mason, who is married, resigned last week.
"My only plans are to focus my full attention on my precious children and my husband who I love dearly," she said in a statement issued by Bentley's office. "They are the most important people in my life. Thank you for your prayers for our family."
How states handle recalls
Nineteen states and the District of Columbia permit the recall of state officials, according to the National Conference of State Legislatures.
Alabama isn't one of them.