The health of Jerry Collins' baby daughter has improved, but she remains in hospital in France in a critical condition.
The former All Black captain and his partner Alana Madill died in a car crash in France, yesterday.
Their young daughter, Ayla, survived the crash, but is still in hospital.
Speaking on behalf of Collins family, his agent Tim Castle, said Ayla's condition has slightly improved.
He said the family was thankful for the outpouring of support following the death.
Mr Castle said Collins' cousin and former All Black Tana Umaga has been helping from Italy, and his French club Narbonne were offering support on the ground.
Police in France said the crash happened on the A9 motorway near Montpellier.
They said it was believed the couple's car crossed the motorway median barrier and collided with a bus.
Collins, 34, who played 48 tests for the All Blacks and captained them three times, was in France playing for second-division side Racing Club Narbonne.
We are shocked and saddened by reports about the accident involving Jerry.— All Blacks (@AllBlacks) June 5, 2015
The Ministry of Foreign Affairs and Trade said an adviser from the Embassy in Paris would travelled to Montpellier to assist with the process of bringing his body back to New Zealand.
The ministry said it would be a matter for local authorities to determine how the crash occurred.
The New Zealand Embassy in Paris is in contact with local authorities and consular assistance will be provided to family in New Zealand.
'Extraordinary leader and player'
Hurricanes CEO James Te Puni said the team was shocked and saddened to hear about the deaths of Collins and his partner.
"He was an extraordinary leader and player, and our thoughts and prayers go out to his family at this time."
Mr Te Puni said the team, and fans, would be praying for Ayla's recovery.
The Hurricanes wore black arm bands during last night's match against the Highlanders in Napier, and a moment of silence was also held before the game.
The team found out about Collins' death just before boarding the team bus in Napier, to travel to their Super Rugby game against the Highlanders.
Captain Conrad Smith admitted the news made it hard to concentrate on their job last night.
"It was a tough game to prepare for after that.
"Sat on the bus, thought I was all right, then in the changing room before the game it was a bit tough.
"A lot of the guys hadn't played with him, but Ma'a, myself and Thrushy and a couple of us have played a lot for this jersey and the Hurricanes and it all knocks you around in different ways.
"I can only speak for myself but it made it into a different game."
Collins' long-standing manager, and spokesperson for the family, Tim Castle, said they were distraught at the death of the much-loved son, brother and friend, and his partner.
Collins, who was born in Samoa, played for the Wellington Lions as well as the Hurricanes, and made his international debut against Argentina in 2001.
After leaving New Zealand, he played for Toulon and the Ospreys before heading to Japan, where he played for Yamaha Júbilo until 2013.
In his profile page on the All Blacks' website, he is described as "one of the toughest and most uncompromising forwards" to ever play for the team.
Rest n peace My brother JC n your lovely lady . You will be surely missed Prayers to your little may she Survive ofa atu colins family.— JONAH LOMU (@JONAHTALILOMU) June 5, 2015
My heart and sadness goes out to jerry's wife and her family. And also to the collins family.. alofa atu!!— Piri Weepu (@piriweepu) June 5, 2015