Assistant coach Rob Howley spoke on behalf of the squad after they arrived in Hamilton for Sunday's World Cup clash against Samoa at Waikato Stadium.
"Our heartfelt condolences go out to the mining community," Howley said. "Mining has been a huge tradition in Wales.
"Our thoughts are with all the families and friends who have been through a difficult time in the last three or four days."
Meanwhile, the Ospreys, who have several players in New Zealand with Wales, were due to wear white armbands on their black strip in Satudayday's away league game against Italian side Benetton Treviso.
"The thoughts and prayers of everybody at the Ospreys are right now with all those involved with the events at Gleision Colliery, especially the families of the four miners," Ospreys chief operations officer Andrew Hore said.
"The tragic scenes have had an effect on everybody here, as they have across the country and beyond, and the small gesture of wearing armbands is the players' way of showing support for the local community."
The Ospreys will hold a one-minute silence ahead of their game against Ulster in Swansea next weekend, paying respect to Charles Breslin, Phillip Hill, Garry Jenkins and David Powell, who all lost their lives in the tragedy.
On the field, Samoa will hope World Cup history can again work in their favour and help them to register another famous win.
Samoa beat Wales on their previous two World Cup meetings in 1991 and 1999, and a third success would leave Wales facing a probable pool stage exit.
Samoa skipper Seilala Mapusua said: "Wales are the favourites, make no bones about it. They are ranked ahead of us in the International Rugby Board rankings.
"Hopefully the pressure is on them. We are one of the minnows and we hope to upset them. We've put a bit of pressure on ourselves as well - we've got no excuses.
"Knowing that a small nation can perform on the big stage has been an inspiration in the past.
"I remember the 1991 game. Growing up, To'o Vaega was one of my idols as a youngster and seeing him score that try (against Wales), I just remember being really excited.
"A Samoan kid growing up in New Zealand watching Samoa in the World Cup for the first time it was quite special, and I've never seen my parents so proud to be Samoan."
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