Mr Rowley today rejected suggestions of scheming against Ms Dugdale, who quit as leader last month, and said he was "disappointed" over the emergence of the "private conversation" from Labour's Autumn conference this week.
Former Labour MP Gemma Doyle today called on Mr Rowley to consider his position in light of the latest revelations.
But asked at Holyrood if he planned to stay on as Deputy leader, Mr Rowley said: "I intend to do that."
He added: "I'm really disappointed that what I thought was a private conversation was tape recorded.
"I believed that to be a private conversation and the point is that I now need to move on with what I'm doing.
"We have a party that wants to unite, we have a membership that wants us to get on with the job in hand and that's what we all need to do. We need to pull together, have this election and move forward."
Party economy spokeswoman Jackie Baillie had accused Mr Rowley of "plotting" over the revelations of the tape which indicate he was in discussions with MSP colleagues about Ms Dugdale's leadership. The former leader herself yesterday said it pointed to "internal problems" in the party.
Nicola Sturgeon attacked labour at Holyrood over the internal feuding with the party at First Ministers Questions.
"Scottish Labour just fights amongst themselves," the First Minister said.