Supt Norman Haslett was speaking after a family from west Belfast left their home following a threat against their three teenage children.
The level of threats can vary, Supt Haslett told the Stephen Nolan Show.
Trevor Lunn, the Alliance party's justice spokesman, said the threats showed paramilitaries were still active.
"It's a very depressing statistic," he said.
"It gives the lie to any suggestion that paramilitaries organisations have gone away.
"They're still taking the law into their own hands issuing these threats.
"It's disgraceful".
Northern Ireland police deal with one paramilitary death threat every day, a senior officer has told the BBC.