The government is probing militant links to last month's mutiny
The head of police in the Bangladeshi capital Dhaka has met the principals of several English-language schools to discuss threats made against them.
The private school principals say they fear the threats are coming from Islamic militants and have requested more police protection.
Police said the "veiled threats" had come in letters and telephone calls.
The government is still investigating whether last month's border guard mutiny had an Islamic militant element.
The mutiny resulted in the deaths of 74 people.
Dhaka Police Commissioner Shahidul Haque told the BBC Bengali service that several language schools had received veiled threats the police were investigating.
He said that the police had urged about 100 privately owned language schools in Dhaka to use more private security guards to ensure they had the maximum protection. Parents of pupils have been made aware of the threat.
Correspondents say that the vague nature of the threats makes it impossible to say conclusively that they have come from Islamic radicals.
Even so the schools themselves - along with parents - are not taking them lightly.
"I got very scared... and picked up my son before classes were over on Thursday," the father of one 14-year-old boy told the Reuters news agency.
"I am talking with other guardians [about whether] we should send children to schools after the weekend."
Security has been increased across Dhaka since the mutiny, especially at the offices and residences of politicians and at government-run schools.
It is estimated that about 100,000 students in Dhaka attend private English language schools, which charge higher fees than Bengali-language schools.
The government says that it will soon release the findings of an official probe into the 25-26 February revolt, which some have blamed on the Jamayetul Mujahideen Bangladesh (JMB) extremist group.
The JMB carried out a series of bombings across the country at the same time in 2005.