National security spokesman Mike Omeri said four towns had fallen since last Friday, including three in Borno state and Buni Yadi, in neighbouring Yobe, where the insurgents slaughtered more than 40 students in February last year before seizing it in August.
Crucial "co-operations and alliances" have led to victories over the Islamist rebels, he said, thanking neighbouring Cameroon, Chad and Niger for cutting off "the supply lines of the terrorists".
"It is hoped that the unfolding regional cooperation will hasten the total defeat and extermination of Boko Haram in Nigeria and the sub-region," he added.
Since the unprecedented joint offensive was launched last month, Nigeria has maintained that its troops were controlling operations.
But witnesses, experts and claims by other militaries indicate that Chadian troops have made a particularly large contribution, advancing deep into Nigerian territory and flushing Boko Haram fighters out of several parts of Borno state.
Nigeria delayed its February 14 general election to March 28 after security chiefs said they needed more time to weaken the militants.
The reported successes, which have not all been independently verified, may allow more people to vote across Boko Haram's northeast stronghold.
As a result, President Goodluck Jonathan's re-election chances could improve if voters feel he has finally taken decisive action against the rebels.
The conflict has killed more than 13,000 people since 2009, and critics have accused Jonathan and military top brass of failing to contain the violence.
The fighting has displaced more than 1.5 million people in Nigeria but Omeri claimed that some were "now returning to their homesteads to settle back into normal life".
There was however no independent confirmation of significant numbers of displaced people returning home and Nigeria's claims about the conflict have in the past not been consistent with reports from the ground.
The International Committee for the Red Cross on Tuesday warned of a "full blown humanitarian crisis" in the Lake Chad region, where Nigeria meets Niger, Chad and Cameroon.