Jeremy Browne, the Lib Dem crime prevention minister, estimated that one in six women is pursued by a stalker at some point in their life, with some feeling their lives have been "ruined" by the crime.
He said two new offences that came into force on Sunday will make it "clear" stalking will be prosecuted by police. Those convicted of stalking by harrassing, following or spying on people face up to six months in prison, while those guilty of stalking with the threat of violence face up to five months in jail.
"It is the sort of offence that people can sometimes brush under the carpet, not be aware of," he said.
"It is something that has been trivialised in the past as just people, mainly women being a bit bothered but nothing to worry about too much.
"But we're saying it is a serious offence, it is a significant offence, we want people to be aware of it. Where it comes with the threat or the fear of a threat of violence associated with stalking then that is an even more specific offence that comes with heavier penalties.
"I think that police forces around the country will now have this as a very clear guide of how the Government wants them to deal with this offence."
Mr Browne said there is some evidence that making stalking a specific offence helps convict more people, after Scotland brought in similar laws two years ago.
At the moment, around 120,000 women are stalked each year but only half lead to a reported crime and only one in 50 incidents leads to a conviction.
Theresa May, the Home Secretary, said over the weekend she had moved to address weaknesses in the current system after hearing from a mother whose daughter was killed by her stalker.
Rana Faruqui, a 35-year-old business analyst was stalked and then stabbed to death in 2003 by a former boyfriend, Stephen Griffiths.
Miss Faruqui's mother Carol became a campaigner for tougher laws on stalking.
The Home Secretary said over the weekend: "Carol was determined to campaign for the victims of stalking and talking to her made me realise the full horror of stalking. I am determined to do all I can to stop more women suffering Rana's fate. Sadly her case is not a one-off."