Federal Justice Minister Rob Nicholson said Thursday he has no plans for an inquiry, a decision Dexter said his government will try to change.
"The facts of the case are deeply disturbing, so why would you not agree to some kind of review?" Dexter said.
He said the province's request for an inquiry was not intended to assign blame.
"Whenever there is a failure in a system there is a tendency in that system to want to defend themselves. That's not the function of a review and that is not what politicians should be doing."
On Tuesday, the Supreme Court of Canada rejected the Crown's appeal of a lower court ruling that tossed out 17 sex offence convictions against MacIntosh.
The court said the provincial Crown took too long to bring the former Cape Breton businessman to trial on charges involving boys in the 1970s.
MacIntosh was working in India when the allegations first surfaced in 1995, but he wasn't extradited to Canada until 2007 and didn't go to trial until 2010.
Nicholson said Thursday that when the federal Conservatives came to power, they acted swiftly to have MacIntosh extradited.
"This matter was expedited after we came into office," he said. "A request for extradition was made in July of 2006 and within a year the individual was returned to Canada."
Dexter had said the provincial government was willing to co-operate if Ottawa decided to examine the circumstances surrounding the delay in getting MacIntosh back to Canada.
He said he will continue to approach Ottawa to see if there are other options to address the MacIntosh case, which he believes has shaken the public's confidence in the justice system.
Nova Scotia is conducting its own review of how the case was handled by its Public Prosecution Service. A report is expected to be provided to Justice Minister Ross Landry next month.
"We want to see how that is going to turn out, but by no means will that necessarily be the end of the story," Dexter said.
Both of Nova Scotia's opposition parties said Nicholson's response had switched the onus back to Dexter.
Liberal justice critic Michel Samson said the premier should call an immediate public inquiry.
"The premier should be calling the federal government and say I'm doing this ... but with or without you Nova Scotians deserve answers."
Progressive Conservative Leader Jamie Baillie said the delay in calling an inquiry doesn't serve the public interest.
"This need not be complicated. It shouldn't involve two levels of government pointing the finger at each other to see who will go first," he said.
A complainant in the MacIntosh case as well as the Sexual Abuse Network of Canada have called for an external review to find out what happened.