"Question time is to hold the Government of the day to account. The Green Party prefers to not ask patsy questions," Shaw said today.
"We are focused on supporting our Government's response on Christchurch – gun control laws, Royal Commission of inquiry and ensuring people directly affected get all the help they need."
But a National Party spokesperson said it wasn't a rejection of the Greens' question, it was a "House management issue".
Each Question Time, political parties are assigned a certain number of supplementary questions they are able to ask in addition to their primary question.
For example, yesterday National had seven primary questions and 38 supplementary questions – the bulk of which went to Leader Simon Bridges.
The National spokesperson said if the party had accepted the question from the Greens, it would mean it would have had to spread the same amount of supplementary questions over an increased number of primary questions.
This, the spokesperson said, would give MPs less of an opportunity to continue a line of questioning through supplementary questions.