In the past week Timorese Facebook users have filled the popular social media site with photographs about alleged terrorist suspects living in Timor-Leste.
Hornai said “several arrests” had been made of people sharing the “fake news.”
"Do not consider the information in social media is true, it is a lie," Hornai told reporters.
He said Timor-Leste was a tolerant country where people of all religions should be respected.
He called on the general public to stop sharing posts on social media about alleged terrorism in the country.
The comments come as a heavy police presence was stepped up around churches and at the bishop's palace in Dili last week, including Sunday Masses, with both uniformed and plain-clothed officers armed with machine guns.
The terrorism warnings came after members of a single family launched suicide attacks on three churches in Surabaya, Indonesia.