Prime Minister Justin Trudeau should recuse himself from having anything to do with choosing Canada's next ethics watchdog, says a Conservative member of Parliament's ethics committee.

Pat Kelly said he is concerned about the prospect of the prime minister helping to choose a new ethics commissioner while under investigation by that office for his trip to the Aga Khan's private island in the Bahamas.

"Some may view a conflict there, whether there is one or not," said Kelly, MP for the riding of Calgary Rocky Ridge. "It's a very unfortunate situation."

Under the government's rules, the prime minister is the minister responsible for the Office of the Conflict of Interest and Ethics Commissioner.

The Prime Minister's Office is not saying what role, if any, Trudeau will play in choosing the next ethics commissioner.

"We recognize and respect the commissioner's role," wrote spokesperson Andrée-Lyne Hallée. "The government has implemented a new open, transparent and merit-based process for appointments. No decision has yet been made regarding this position."

Kelly's comments came after Mary Dawson, the current ethics commissioner, told the access-to-information, privacy and ethics committee that she is "struggling" to complete her office's open investigations before her term ends July 8. That includes her investigation into Trudeau's controversial vacation to Bell Island in the Bahamas.

If the investigation is not completed by then, it will be up to her successor to decide whether to continue the investigation, start again from scratch or scrap it altogether, Dawson told the ethics committee.

Running out of time

The Trudeau investigation is one of three files Dawson said she is hoping to conclude before she leaves. A fourth file, involving Bruce Carson, a former adviser to Stephen Harper when he was prime minister, will likely take longer to resolve because it has to wait until a court case is concluded.

Conservative MP Pat Kelly, a member of the ethics committee, says the prime minister would appear to have a conflict if he appointed an ethics commissioner who would subsequently be investigating him. (House of Commons)

There is no provision in the ethics commissioner's office rules that allows a commissioner to finish an investigation once a new commissioner begins, Dawson told MPs.

Dawson is conducting an investigation into the Bahamas trip following complaints that Trudeau violated government rules, which prohibit the prime minister, cabinet ministers and parliamentary secretaries from accepting free travel on non-commercial chartered or private aircraft without prior approval from the ethics commissioner.

Trudeau has defended the decision, maintaining that hopping aboard the Aga Khan's helicopter was the only way to get to Bell Island. However, a Privy Council technician, who travelled to the island to set up a secure office for Trudeau, got there on a commercially chartered seaplane.

Trudeau may be the first sitting prime minister to be under investigation by the ethics commissioner while called upon to choose the commissioner's successor.

After several short-term renewals, Dawson's term as conflict of interest and ethics commissioner is now scheduled to end in two months. Her successor has not yet been announced.

Prime Minister Justin Trudeau is under investigation by the ethics commissioner's office for his vacation on the Aga Khan's private island in the Bahamas. (Sean Kilpatrick/Canadian Press)

Dawson was the first person to occupy the position. This will be the first time one ethics commissioner has taken over from another and the first time the office will have to deal with transition questions such as what to do with investigations begun by their predecessor.

Although Dawson said her successor could theoretically choose to drop her investigation if it isn't completed on time, she said the new commissioner would likely have to explain their decision.

"They could discontinue it.… but probably they would have to explain why in a report," Dawson said in an interview with CBC News after the hearing.

Dawson said she is not yet certain whether she will be able to complete the investigation into Trudeau's vacation in the two months remaining.

"I don't have total control over that. It could be doable. It's just a question of how quickly we can get all the evidence we need and how long it takes us to go through it. We're working at it, but you never can tell what you might hit in the middle of it. You might want to have to investigate a little bit further. But I'm trying my best to do it as quickly as I can."

Elizabeth Thompson can be reached at elizabeth.thompson@cbc.ca