Comrade Akaash's statement comes after the rebels were blamed for Friday's train crash which left 148 people dead.
Police say Maoist rebels sabotaged the track, causing the derailment of the Calcutta-Mumbai express in West Bengal.
Maoists denied the charge. But Comrade Akaash also said they would investigate whether any rebels were involved.
Railway officials in eastern India have cancelled night trains in Maoist-affected areas after Friday's incident.
Comrade Akaash told the BBC that they were "appealing" to the railways to run trains through rebel strongholds even during the night.
Profile: India's Maoist rebels
In pictures: India train collision
"We are promising total security to all trains. We will not allow anyone to attack any train anywhere in the country and those trying to do it will face stern punishment," he said.
The railways have not reacted to the statement.
Police say they have "definite evidence" that a local rebel Maoist militia were behind the disaster - they have named two militia leaders as the prime suspects.
One of the suspects, Umakanta Mahato, was arrested last June and charged with sedition and waging war against the state.
But he was released on bail in December, and the police did not contest the bail, court records say.
Independent lawyers are asking why the police did not contest the bail plea of a senior Maoist militia leader.
Railway officials in eastern India have cancelled night trains in Maoist-affected areas after Friday's incident.
The restrictions would be in place until 0500 [2330GMT] on 3 June, the company said.
Report said other services were being rescheduled to ensure they travelled through Maoist areas of eastern India in daylight.
Prime Minister Manmohan Singh has described the Maoist insurgency as India's biggest internal security challenge.

Jonathan Platt successfully contested a fine from Isle of Wight Council for taking his young daughter on a family holiday to Florida in April.
He will now speak up on behalf of other parents when the council seeks High Court clarification on the law.
He is crowdfunding for Â£25,000 expected legal costs and raised more than Â£1,000 in the first 24 hours.
The father wrote on the fundraising page he would spend the money on "nothing other than legal fees for solicitors and barristers".
He added: "I will take nothing personally from the money, not even travelling costs."
Isle of Wight Council is asking the High Court for clarification on what constitutes "regular" attendance at school. As Mr Platt is a "person of interest" in the case, he has a right to attend.
He said he is arguing "on behalf of all parents".
Comments on the online crowdfunding page include: "Thank you for being our voice Jon, we are all behind you."
"Well done and good luck, let's hope common sense prevails."
Mr Platt took his children to Disneyland in Florida in April despite his daughter's absence being refused by her primary school.
The council took him to court after he refused to pay a Â£120 fine.
He won his case after he told magistrates that Section 444 of the Education Act did not put restrictions on holidays during term time, provided pupils otherwise attended school regularly.
The council has applied to the High Court for an opinion on whether "the unauthorised absence of a child for seven consecutive school days on holiday... amounts to the child failing to attend the school regularly".
A Maoist leader in India has said that they will take "full responsibility" for the safety of trains travelling through areas under their control.
[NEXT_CONCEPT]
A father is preparing for a High Court legal battle to give parents the right to take children on term-time holidays.