Governor speaks out over massacre
He said in an address on Saturday night that what is important right now is "love, courage and compassion".
Friday's massacre at Sandy Hook Elementary in Newtown in the state killed several adults and 20 children aged six or seven. A medical examiner said the victims were shot by a rifle multiple times.
Police are trying to learn more about the 20-year-old gunman, who also killed his mother and himself.
After the shooting, Mr Malloy went to a firehouse where victims' relatives gathered.
He said "evil visited" their community of about 27,000 people 60 miles north-east of New York City. He said since then love has "poured in from around the world".