The bill sets 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.
Flag Minister Bill English hit back at Labour saying it was Labour's 2014 policy to hold a similar process but it was opposing it because they do not like John Key.
He said Labour liked to pride itself on being "the owners of New Zealand" and its national identity.
"That may have been the case when Michael Joseph Savage was the Prime Minister, but in this intellectually bankrupt, unaspirational, modern Labour Party it does not own any aspect of our national identity."
Green Party MP Russel Norman said the Prime Minister only wanted the "optics" of changing the flag.
However, he said steering clear of wider constitutional issue was a failure of leadership. "By changing the flag, what do we really change? ... It's just changing a piece of cloth."
He said Mr Key simply wanted a fourth term as Prime Minister and rejected the argument that a change of flag would celebrate New Zealand's independence from Britain.
"Actually, it will do nothing of the sort. The head of State will still be a British person."
The Flag Referendums Bill returned to Parliament on the same day Gareth Morgan announced the winner of the $20,000 prize for his flag design contest.
That was won by design studio Studio Alexander for an abstract flag with geometric shapes in red, blue, white and black - see it here.
Mr Morgan is campaigning to change the flag and said he wanted a design which reflected the Treaty of Waitangi. The winner will also be displayed on a billboard.
The official Flag Consideration Panel is expected to release a long list of alternative designs from the 10,000 submitted next month before whittling those down to the four designs that will be voted on in a referendum in November.
Five things about the national anthem:
1. In 1876, God Defend New Zealand - A National Hymn was first published as a poem in Dunedin newspaper, the Saturday Advertiser. It was written by the paper's editor, Thomas Bracken.
2. Head teacher of a Catholic school in west Dunedin, John Joseph Woods, won a competition to find who could compose the best music to accompany the poem. The competition prize was 10 guineas, or roughly $1500 in 2015.
3. On Christmas Day in 1876, God Defend New Zealand was first performed in Dunedin's Queen Theatre by the Lydia Howarde Burlesque and Opera Bouffe Troupe. They were accompanied by the Dunedin Royal Artillery Band.
4. God Defend New Zealand was declared an official national anthem, alongside God Save the Queen, in 1977. Pressure for it to be nominated as a national anthem grew as sports became popular following World War II.
5. A Maori translation of the anthem, Aotearoa, first appeared in Otago newspapers in October 1878.
(Source: Te Ara, The Encyclopedia of New Zealand)
A timeline of God Defend New Zealand's journey through Parliament:
1897 - Queen Victoria is presented with a copy of words and music for God Defend New Zealand by Prime Minister Richard Seddon.
1939 - A request to make God Defend New Zealand the country's national song in time for the Centennial Year is considered by Cabinet.
1940 - Prime Minister Peter Fraser declares God Defends News Zealand as the national song of New Zealand.
1973 - Prime Minister Norman Kirk attempts to make God Defend New Zealand the country's national anthem but is unsuccessful.
1976 - A petition is presented to parliament on November 3, asking that God Defend New Zealand becomes New Zealand's official national anthem.
1977 - Internal Affairs Minister David Allan Highet announces on November 21 that the national anthems of New Zealand would be the traditional anthem, God Save The Queen, and the poem, God Defend New Zealand. Queen Elizabeth II gives her consent.
(Source: Ministry for Culture and Heritage)