If fewer than half of eligible voters take part in the first flag referendum the second should be scrapped, Labour say.
Parliament has this week debated the Flag Referendums Bill, which will set up the two referendums on the flag - the first to vote on an alternative design and the second for voters to choose between the alternative and the current flag.
Labour is opposing the bill despite leader Andrew Little's own desire for a new flag and its 2014 policy to start the process to secure that change.
Mr Little said that the reaction from the public meant the party did not believe the time was right to change the flag.
"Today we have added two Supplementary Order Papers to the flag referendum bill, one seeking to defer the referendum for five years and the second to stop the final referendum if voter apathy continues at its current level.