Alward announced that the byelection for the eastern riding of Kent will take place on April 15, a week after Graham vacated the seat.
Graham quit politics after he was found to be in a conflict of interest over a $50-million loan guarantee his government gave to a construction firm in 2009.
The province's conflict of interest commissioner said the former premier should have removed himself from the cabinet discussions about the loan guarantee to Acton because it had ties to his father.
"I believe (voters) will have an opportunity to really send a verdict to the Liberal party for their handling of the Atcon scandal," Alward said Monday.
But Liberal Leader Brian Gallant, who is running in the byelection, said it will be about the track record of the governing Progressive Conservatives.
"Our economic indicators have all worsened ever since Mr. Alward has taken office, whether it be our population growth, job creation, unemployment, the economy or the deficit and debt, Gallant said in an interview.
"It is very clear to me going around the riding and the province that New Brunswickers and the people of Kent are fed up and want our province to be back on the right track."
The Tories will choose their candidate on Wednesday.
Shortly after Gallant was chosen as party leader in October, the Tories offered not to oppose him if he wanted to seek a seat in the legislature. But Alward said Monday the circumstances have changed since that offer was made, adding that Gallant declined the offer.
"He said Shawn Graham was going to stay there until the end of this mandate," Alward said. "It's clear Shawn Graham has had to step down in scandal."
Gallant defended Graham, saying he stayed on as the member for Kent to allow the conflict of interest commissioner to complete his investigation.
"Most would agree that it is commendable for New Brunswickers to be able to see the report," Gallant said. "Four days after the report came out he decided that he would step aside."