Loose forward Kaino and wing Savea were among 10 All Blacks who posed for a picture with the sign #SamoaUnited. An additional message on Instagram said: "Players staying United for Manu Samoa and a positive outcome for the future of Samoan Rugby."
The other players involved were Dan Carter, Sonny Bill Williams, Patrick Tuipulotu, Brodie Retallick, Charlie Faumuina, Augustine Pulu, Liam Messam and Keven Mealamu.
The message came after the Samoan team threatened to boycott this weekend's test against England at Twickenham in order to leverage a meeting with its union due to concerns about its governance and administration. It is the result of long-running issues, with Kaino and Savea hoping their support can force the problems to be resolved.
It is understood the All Blacks management accepted the players's actions, although Kaino said the players didn't inform them of what they were planning.
"I'm sure the coaches would have supported me if I had gone up to them and asked them ... but I didn't run it past any of the management because I didn't think it was much of a big deal. It's just brothers supporting brothers," Kaino said today.
"I'm a proud Samoan, it was just a bunch of brothers showing their support for a bunch of other brothers in the Samoan team. We just wanted to let them know we support what they're doing.
"It's important to me. I've known what they've been going through; really it's us putting our weight behind what they've been doing, to show that we support them.
"I'd like for the Samoan boys to be happy with their situation and their administration and their team. If they're happy then we'll be happy. I'm good friends with a lot of the guys in their set-up. They've made it known that they're frustrated and the reason behind that picture was to show that we support what they're doing.
"They've got a lot of talent and potential in their team. If they could get all the bases covered then I'm sure it would flow on to their performances on the field."
Savea said: "It's just us supporting the players. Everything else is up to them and their union."
- By Patrick McKendry of NZME. News Service in Cardiff
