Fakruddin and Bilal Mallick, close associates of slain terrorist Imam Ali, had started hatching the conspiracy as the schedule of Advani's yatra was announced last month, they said.
The STF suspect that the two were hiding in either Bengaluru or Andhra Pradesh and special teams have been sent there for investigation, the officials said.
Fakruddin, son of a retired police constable, was involved in a blast case at Ovamalai in the district in 2002, in which Imam Ali was arrested. He had helped Ali to escape when he was being taken to Palayamkottai prison. Ali, a dreaded terrorist, was killed in an encounter in Bangalore in 2002.
Bilal Malik was one of the accused in the murder of Hindu Makkal Katchi leader Kalidass five years ago. When he was in Vellore prison he had attacked the jailor and a case was still pending, the police said.
A powerful pipe bomb was unearthed from under a bridge and defused on October 27 at Alampatti village, about 30 km from here, on the route of Advani's yatra.
The police on November 1 arrested Ismath and Abdullah Rahman, both city residents, and detained one Usman Ali on Wednesday in connection with the incident.
STF officials said Ismath and Rahman were only perpetrators who had given their vehicles. "It was information about the motorbike of Ismath, a watermelon seller, which was noticed continuously for three days on the bridge at Alampatti, that helped police to nab the two culprits," they said.
Fakruddin and Mallick had taken the help of Ismath and Rahman, thinking police would not suspect them as they were not in any organisation.Rahman had helped in hiring an autorickshaw to bring the explosives without raising any suspicion.
"Only if Fakruddin is arrested, we will know from where they had procured the lethal chemical 'Power Gel90' and other details," the officials said, adding that the police were confident of arresting the two in a week's time.
