Crime prevention minister Jeremy Browne says the introduction of new legislation making stalking a criminal offence will stop the issue being "brushed under the carpet".
Speaking on BBC Breakfast, he said:
It is the sort of offence that people can sometimes brush under the carpet, not be aware of, it has been trivialised sometimes, I think, in the past as something which is just people, mainly women, being a bit bothered but nothing to worry about too much.
This is a very serious problem which affects thousands of thousands of mainly women, not exclusively women, but mainly women, right across the country.
Victims and Equalities Minister Helen Grant said creating new stalking offences will ensure "victims of this heinous crime are better protected and will bring more offenders to justice".
Ms Grant said:
The Government's ambition is nothing less than ending all forms of violence against women and girls.
But we must also ensure that if people's lives are affected by crime, the right kind of help or support is available.
For the first time we have made sure nearly £40 million of Central Government funding is in place for organisations that do so much to help victims, often with so little.
New laws designed to give extra protection to victims of stalking have come into force.
The Government is also providing new support aimed at reducing domestic and sexual violence and female genital mutilation (FGM).
Two specific criminal offences of stalking have come into force in England and Wales for the first time.
This is part of a package of new funds and measures to crack down on abuse leading into the 16 days of action that follow yesterday's UN International Day for the Elimination of Violence Against Women.
Stalking is an appalling crime that destroys lives. The impact on victims can be devastating and we are doing all we can to make sure they have the protection they need and do not have to live in fear.
These new offences send a clear message to offenders that stalking is a serious crime and they will be brought to justice for making others' lives a misery.
A victim of stalking has created a mobile phone application that alerts family and friends if someone is in danger.
The innovation comes as the Government has introduced two new criminal offences today, stalking and stalking involving a fear of violence.
Stalking has been made a specific criminal offence in England and Wales in a move to improve the safety of victims.
Under the new Protection of Freedoms Act 2012, the Government has introduced two offences, stalking and stalking involving a fear of violence.
Previously, the Protection of Harassment Act 1997 did not specifically name stalking as an offence, instead citing two criminal offences of harassment.
An inquiry into stalking earlier this year by Parliament found that around 120,000 people are victims of stalking every year.
Today on International Women's Day, the Government announced plans to make stalking a specific criminal offence.Read the full story ›
Happy International Women’s day. My advice to young women: educate yourselves, work hard, be brave, and help each other.
Shadow Home Secretary Yvette Cooper said: “We have been campaigning for a new law on stalking for some time so it is welcome that the Government has accepted that changes are needed.
"However I am worried their plans do not go far enough, and are not strong enough. Their proposals risk being half-hearted and over-complicated, so victims won't get the protection they need."
The government has denied reports that the new European legislation to outlaw violence against women would mean a ban on wolf-whistling. A spokesman said:
"We are talking about a serious issue of harassment and stalking and domestic violence and abuse. Millions of women across Europe suffer from violence and abuse. By signing this convention, we are ensuring that British offenders who commit offences abroad will face justice in our courts."