It also asked the local government ministry and city corporations create social awareness on the issue.
The meeting in the PMO was convened on the directions of Prime Minister Sheikh Hasina who is in UK for eye-treatment.
Bangladesh has been awash with rumours that a group of child lifters is kidnapping children as human head is required for the successful completion of the Padma bridge.
Eight people have been killed in incidents of mob lynching sparked by these rumours over the last few days.
Earlier on Wednesday, Bangladesh Inspector General of Police Mohammad Javed Patwary said that 31 cases have been registered and 103 people arrested.
He said 60 Facebook accounts, 25 YouTube links and 10 online news portal have been shut down to check the rumours.
Local Imams have also been asked to caution people against the rumours during their sermons.