Story highlights Mexico's President says he hopes the arrests will help solve the case

43 students, mostly young men studying to be teachers, were allegedly abducted 39 days ago

Official called Mexican mayor, wife along with police chief the probable "masterminds"

The mayor and his wife had been missing since the September 26 incident

A Mexican mayor characterized as a "probable mastermind" in the mass abduction of 43 students has been taken into custody as authorities have tracked down a top target who eluded them for weeks -- even if they still haven't managed to locate the missing.

Iguala Mayor Jose Luis Abarca and his wife, Maria de los Angeles Pineda -- dubbed "the imperial couple" by local media for how they presided over their southern Mexican city -- were detained early Tuesday morning at a house they had rented in Mexico City's Iztapalapa neighborhood. They did not resist arrest, authorities said.

The couple had been staying in a house that appeared to be abandoned, and investigators first got suspicious when they saw a woman repeatedly entering and leaving the building, Mexican Attorney General Jesús Murillo Karam told reporters. That woman, Noemí Berumen Rodríguez, was arrested alongside the mayor and his wife. Authorities accused her of concealing the couple.

Their capture, which Mexican Federal Police spokesman Jose Ramon Salinas reported on his Twitter account , signals a major milestone in the high-profile case.

"I hope that this detention contributes in a decisive way to solving the investigation that the Attorney General's Office is conducting," Mexican President Enrique Peña Nieto said as he praised authorities for the arrests Tuesday.

Photos: Photos: Missing Mexican students Photos: Photos: Missing Mexican students Missing Mexican students – Forty-three students remain missing after armed men ambushed buses carrying students in southern Mexico on on September 26 .The Mexican state of Guerrero posted images and offered a reward of 1 million pesos ($74,000) for information leading to the missing students. Images of three missing students were not available. Hide Caption 1 of 41 Photos: Photos: Missing Mexican students Hide Caption 2 of 41 Photos: Photos: Missing Mexican students Hide Caption 3 of 41 Photos: Photos: Missing Mexican students Hide Caption 4 of 41 Photos: Photos: Missing Mexican students Hide Caption 5 of 41 Photos: Photos: Missing Mexican students Hide Caption 6 of 41 Photos: Photos: Missing Mexican students Hide Caption 7 of 41 Photos: Photos: Missing Mexican students Hide Caption 8 of 41 Photos: Photos: Missing Mexican students Hide Caption 9 of 41 Photos: Photos: Missing Mexican students Hide Caption 10 of 41 Photos: Photos: Missing Mexican students Hide Caption 11 of 41 Photos: Photos: Missing Mexican students Hide Caption 12 of 41 Photos: Photos: Missing Mexican students Hide Caption 13 of 41 Photos: Photos: Missing Mexican students Hide Caption 14 of 41 Photos: Photos: Missing Mexican students Hide Caption 15 of 41 Photos: Photos: Missing Mexican students Hide Caption 16 of 41 Photos: Photos: Missing Mexican students Hide Caption 17 of 41 Photos: Photos: Missing Mexican students Hide Caption 18 of 41 Photos: Photos: Missing Mexican students Hide Caption 19 of 41 Photos: Photos: Missing Mexican students Hide Caption 20 of 41 Photos: Photos: Missing Mexican students Hide Caption 21 of 41 Photos: Photos: Missing Mexican students Hide Caption 22 of 41 Photos: Photos: Missing Mexican students Hide Caption 23 of 41 Photos: Photos: Missing Mexican students Hide Caption 24 of 41 Photos: Photos: Missing Mexican students Hide Caption 25 of 41 Photos: Photos: Missing Mexican students Hide Caption 26 of 41 Photos: Photos: Missing Mexican students Hide Caption 27 of 41 Photos: Photos: Missing Mexican students Hide Caption 28 of 41 Photos: Photos: Missing Mexican students Hide Caption 29 of 41 Photos: Photos: Missing Mexican students Hide Caption 30 of 41 Photos: Photos: Missing Mexican students Hide Caption 31 of 41 Photos: Photos: Missing Mexican students Hide Caption 32 of 41 Photos: Photos: Missing Mexican students Hide Caption 33 of 41 Photos: Photos: Missing Mexican students Hide Caption 34 of 41 Photos: Photos: Missing Mexican students Hide Caption 35 of 41 Photos: Photos: Missing Mexican students Hide Caption 36 of 41 Photos: Photos: Missing Mexican students Hide Caption 37 of 41 Photos: Photos: Missing Mexican students Hide Caption 38 of 41 Photos: Photos: Missing Mexican students Hide Caption 39 of 41 Photos: Photos: Missing Mexican students Hide Caption 40 of 41 Photos: Photos: Missing Mexican students Hide Caption 41 of 41

JUST WATCHED Mexican mayor and wife arrested Replay More Videos ... MUST WATCH Mexican mayor and wife arrested 04:16

JUST WATCHED Search for missing students ramps up Replay More Videos ... MUST WATCH Search for missing students ramps up 02:23

JUST WATCHED Ex-mayor linked to missing students Replay More Videos ... MUST WATCH Ex-mayor linked to missing students 02:23

JUST WATCHED Mexico: Where are 43 abducted students? Replay More Videos ... MUST WATCH Mexico: Where are 43 abducted students? 02:50

Yet it's not clear how much closer the arrests get investigators to finding the 43 students, wherever and in whatever state they now are, dead or alive.

The victims were mostly men in their 20s studying to become teachers at a college in rural Ayotzinapa. On September 26, they traveled on buses and vans to nearby Iguala for a protest.

They haven't been seen or heard from since.

Murillo Karam has said that when Abarca, along with Pineda, learned the students' protest would disrupt one of his events, the mayor ordered then-Iguala police Chief Felipe Flores Velasquez to stop the demonstration. Murillo cited information obtained from interrogated police officers and gang members.

Police blocked the highway leading into the city and shot at the students' vehicles, killing at least one student.

Officers then took the remaining students away and, Murillo said, handed them over to a local criminal gang known as Guerreros Unidos. That gang not only had infiltrated the police department but was also complicit with Abarca, his wife and the now-former police chief, according to the attorney general.

Authorities have arrested about 60 suspects, but not the most sought-after ones -- until now.

Abarca and Pineda went missing only hours after the students' reported abduction. On October 22, Murillo said his office had issued arrest warrants for them as well as Flores, who remains at large. He said they were considered "probable masterminds" of the events in Iguala.

The case has spurred protests across Mexico, and the governor of Guerrero state -- criticized for not acting quickly enough after the abductions -- has taken a leave of absence

Rogelio Ortega, the academic tapped to take over for Gov. Angel Aguirre, told CNN en Español last month that Guerrero state faces a tough road in light of the alleged corruption and kidnappings.

"The problem today is how to successfully face these unleashed demons," Ortega said before his selection as interim governor. "How can we rebuild the social fabric?"