A knife amnesty should be introduced "without delay", Opposition parties have said.
The call follows a weekend when three people were seriously injured in stabbing incidents.
Labour Party spokesman on justice Brendan Howlin said he was "horrified at the recent upsurge in stabbings", while Fine Gael justice spokesman Jim O'Keeffe said an amnesty would take a large number of knives out of circulation and "focus minds" on the issue.
The Criminal Justice Bill, which was signed into law last week, empowers the Minister for Justice to call an knife amnesty for "a specified period".
During such an amnesty people may surrender knives "at any Garda station or at any place approved for the purpose by a superintendent of the Garda Síochána".
Surrendered weapons may be forensically examined "for the purpose of discovering information concerning an offence" and the person surrendering it must give their name and address.
While plans are in place for a national firearms amnesty in the autumn, a spokeswoman for the Department of Justice said the Minister, Michael McDowell, was "considering a knife amnesty".
Mr Howlin expressed his "alarm and dismay" at an increase in knife-related crime and "the growing propensity for young people to carry knives".
Mr O'Keeffe said it was "absolutely frightening what's happening and the extent to which carrying a knife is seen as almost normal.
"I would want the Minister to call an amnesty without delay, but also when he is advertising it, to highlight the high penalties for carrying a knife."
Under the 1990 Firearms and Offensive Weapons Act it is illegal to carry "in any public place any knife or any other article which has a blade or which is sharply pointed".
An offence is punishable with a fine of up to €1,200 and/or imprisonment for up to five years.
Opposition spokesmen said they had been struck by the success of knife amnesties in Northern Ireland and Britain this year.
Almost 90,000 knives, machetes, meat-cleavers and screwdrivers were handed in in England and Wales, while 12,600 were surrendered in Scotland during a five-week amnesty in April and May.
In the North a three-week amnesty in May was targeted at males in the 11 to 18-year-old age group amid concern about a growing knife culture.
In this State last year criminal proceedings were taken in 2,107 cases where a knife or similar offensive weapon was used, almost half of which were in the Dublin metropolitan region.
A Sinn Féin councillor in Tallaght, Mark Daly, said some young men consider it "almost fashionable" to carry a knife.
"It has worsened in the past year and the message has to go out that it's neither desirable nor necessary to carry these weapons."
