"It's a very touchy issue," said Councilwoman Debbie Ortega.
"I think the only comment I would make," she said, "is that when we are elected, there is a trust placed in us to lead and to operate in a very ethical manner."
Councilman Rafael Espinoza noted how more people can openly talk about their experiences.
"I'm glad the environment and the culture is such that victims of any sort of sexual harassment feel comfortable speaking out," he said.
When asked if he thinks the mayor should step down, Espinoza replied, "I think that's going to be up to the public."
The District 1 councilman said when he first found out about the allegations Tuesday night, he had a sense of disappointment.
"And the subsequent reading of the expanded texts this morning sort of deepened that," he said.
"I'm very disappointed in the mayor's behavior," said District 2 Councilman Kevin Flynn. "It's completely unacceptable in a workplace. I'm saddened and disappointed."
Flynn said he thinks Mayor Hancock did the right thing by apologizing immediately and by offering to apologize in person to the officer.
"If she's open to that, I would hope that it would go well between them," he said.
Flynn told Denver7 that he doesn't think the mayor should step down because the city's charter requires that a special election be held in such an instance, and that would cost $1.2 million.
He said the earliest there could be a special election would be in late July.
"Frankly, the voters are going to get to weigh in on this next May (2019), anyway," he said.
Flynn added that he had a brief discussion about the issue with another council member earlier Wednesday.
"We shared some opinions about how this, creating a hostile and adverse work environment, is not what we're all about, and whatever we can do to amend that, we should look at," he said. "So I'm definitely onboard with that."
City Council President Albus Brooks put a statement regarding the harassment and Hancock's apology on Facebook:
Robin Kniech said in a statement she was "deeply troubled" by Hancock's actions:
"Sexual behavior in the workplace is disrespectful and disempowering to women, and it is totally unacceptable. Responsibility always lies with the boss to set high standards and to live by them, and I’m deeply troubled by the Mayor’s actions, the environment it created for Detective Branch-Wise and the consequences for our City. It can be confusing and scary to try to navigate what to do about inappropriate behavior in the work place, but no one deserves to feel uncomfortable or intimidated. It is up to us as leaders to make clear that sexual behavior in the workplace is unacceptable, and anyone experiencing it can and should speak up and seek help."