The Mexican political power couple accused of ordering a disturbing police attack on a caravan of unarmed students that left six dead and 43 missing is under arrest, officials in Mexico said Tuesday.

Authorities detained Jose Luis Abarca, mayor of Iguala, Guerrero, and his wife Maria de los Angeles Pineda in a run-down stucco house in Iztapalapa, the poverty-stricken and most populous borough in Mexico City, reports said.

Mexican Attorney General Jesus Murillo Karam said in an afternoon press conference that a third person was detained Tuesday, a woman considered an accomplice to the couple's efforts to evade arrest.

But today officials offered practically no new details on the circumstances of the couple's arrest, other than saying that three groups of investigators were staking out locations in Mexico City and the northern city of Monterrey in the search for the fugitives. Nothing was said about the possible whereabouts of the Ayotzinapa students, who have now been missing for 39 days.

Aquí fueron detenidos Abarca y su esposa en Iztapalapa, DF (+fotos)— Pulso Ciudadano (@PulsoCiudadano_)November 4, 2014

According to early reports, one of Abarca and Pineda's daughters was with the couple at the time of the arrest. Neighbors reportedly alerted authorities that the fugitives were hiding out in a house in the Santa Maria Aztahuacan neighborhood of Iztapalapa that had only a few pieces of furniture and a handful of dogs.

Of the six killed on the night of the police ambush and shooting of the buses, one student's facial skin was removed and eyes were gouged out.

Abarca initially said he was "dancing" on the night of the attack. The mayor requested a leave of absence three days after the September 26 attacks, and then disappeared with his wife.

In the days that followed, federal officials said the mayor's wife was the "chief operator" of a regional drug gang, the Guerreros Unidos, inside Iguala city hall, delivering monthly payoffs of up to three million pesos, or $220,500, directly to the cartel.

Abarca is also accused of personally executing an activist political rival, Arturo Hernandez Cardona, in May 2013, saying, according to witness statements, "I'm going to enjoy killing you myself."

La detención de José Luis Abarca y Ma. de los Ángeles Pineda es parte de las investigaciones para localizar a los 43 estudiantes — Enrique Galindo C (@EF_Galindo)November 4, 2014

The night of the attacks, Pineda scheduled a public party in the city's central plaza to mark her second year in a ceremonial post at the local family welfare agency. It was considered an unofficial launch for her likely campaign to replace her husband as mayor in elections next year.

When word reached the couple that a caravan of students from the Ayotzinapa Normal School was approaching, the mayor used his code name, A-5, officials said, to order the police to prevent the students from approaching and possibly sabotage the event.

Abarca and Pineda became the primary suspects in the disappearance of the students from the Ayotzinapa school, in a case that became a symbol of the depth of narco-linked corruption among Mexican officials. In recent weeks, scores of demonstrators held protests in dozens of cities across Mexico and worldwide calling for the return of the 43 students and an end to corrupted narco-politics in Mexico.

Parents of the missing students — a group that held a disappointing meeting with Mexican President Enrique Peña Nieto at his official residence last week — were headed to Mexico City from Guerrero on Tuesday to meet with federal investigators once more, a parents spokesman told VICE News.

Epifanio Álvarez, father of missing student Jorge Álvarez Nava, 19, said the arrests of Abarca and Pineda "give hope, because we believe the mayor knows where the young men are."

"The prosecutor said last week that they needed to make one more arrest, and we believe he was referring to [Abarca]," Álvarez said. "[Pineda] had a lot do with it. They have to know where they took them and who they turned them over to."

Melissa del Pozo contributed to this report.