"The Prime Minister has previously met members of the quake-victim families. They're more than welcome to extend an invitation to meet again. This will be considered by the office as all invitations are," the spokeswoman said.
A spokesman for Mr Finlayson said he was trying to find time in the next couple of weeks to meet the families.
In the open letter, the Quake Families' group chairmen Brian Kennedy and Maan Alkaisi say they believe most ordinary Kiwis "understand and sympathise with our need to have an independent voice at a commission that has been formed largely in response to our loved ones' deaths".
The counsel assisting the commission and liaison staff will not give them what they need, they say.
"We cannot risk coming out at the end of the commission process feeling that we did not have a voice, that our questions were not asked and answered. We have to find out for ourselves why our loved ones died."
The pair questioned why Pike River mine victims' families had received funding for legal representation, when they had not.
"We can't understand how you can say funding in our case is not justified because our needs are... different to those families."
