However, opponents are disappointed and say National has bowed to political pressure in an election year.
After discussions with Government ministers, National announced yesterday it would support the Criminal Procedure Bill, which will also allow methamphetamine cases to be heard in district courts and allow acquitted individuals to be retried in exceptional cases.
National blocked the Bill in its committee stage because it opposed a clause effectively scrapping oral depositions hearings, leaving the Government with insufficient support to pass the legislation.
National has come under sustained pressure in the past week, with groups and individuals, including Lesley Elliott and Louise Nicholas, criticising its stance on depositions, which they say traumatise victims by making them give evidence twice.
Opposition justice spokesman Simon Power said National would support the Bill with minor changes.
National still had concerns the latter stages of trials could be compromised if the early stages of the court process were not rigorously examined, Mr Power said.
"While this Bill is not perfect, it is a step in the right direction."
Sensible Sentencing Trust chairman Garth McVicar welcomed National's decision and said he had been pushing hard behind the scenes in the past week.
Mrs Elliott said the change sounded like the perfect solution after the trauma her family experienced during the depositions hearing last week for Clayton Weatherston, who is accused of murdering Sophie Elliott at her Ravensbourne home in January.
"There are occasions where I think depositions would be necessary, where there was some doubt about a prima facie case.
I think in our case, and probably in lots of cases, it was clear cut. So why go through this?"
The sister of murdered Kaitangata teenager Michael Hutchings, Sarah Hutchings (17), spent about half a day in the Dunedin District Court dock last month, giving evidence against the two people accused of killing the 18-year-old in early January.
