Black Caps captain Kane Williamson may be considered for their next World Cup match against South Africa on Wednesday night.
Williamson fractured his thumb during their game against Bangladesh just over two weeks ago.
It was his first game back for the national side after seven months on the sideline following knee surgery.
Williamson was struck on the thumb by the ball while running between the wickets and retired hurt.
Coach Gary Stead said Williamson hit balls for the first time yesterday since suffering the injury.
"It's encouraging, it was just low level intensity but he'll train [the next two days] with a view to potentially being available for this game," Stead said.
"That will depend on how well he comes through the nets in the next couple of days."
Fast bowler Lockie Ferguson left the field during yesterday's loss to Australia with an achilles issue and Stead said he will have a scan today.
"We're hopeful that it may just be something that is about a week in terms of return to play."
Mark Chapman didn't play the game against Australia with a calf niggle and Stead said he was progressing well but was not sure if he would be available for selection for the game against South Africa.
South Africa is second on the table with five wins from six games, while New Zealand is third with four wins and two losses.