The referendum runs for the next three weeks, ending Thursday March 24.
Voters will be asked to choose between the current New Zealand flag and Kyle Lockwood's silver fern design selected in the first referendum in late 2015.
The flag that receives the most votes in the second referendum will be the official flag of New Zealand.
"On your voting paper, you will be asked to tick the flag option that you want to be New Zealand's flag," said Mr Peden.
"Make your choice, then get your vote back in the post by 21 March."
Voters should get their voting papers by Friday March 11. Enrolled voters who do not receive their pack by then should visit elections.org.nz or freephone 0800 36 76 56 to get a replacement paper.
They can also request a replacement paper if they make a mistake, lose, or destroy their paper.
Largest and tallest
Auckland Airport is flying both flag options from now until the end of the referendum to help Kiwis make up their minds about which to vote for.
At 72sq m each, the flags are the largest to be flown in the country and they will fly on the airport's 45m- tall flag pole - the county's tallest.
Anna Cassels-Brown, Auckland Airport's spokeswoman, said Auckland Airport was keen to support national debate.
"We hope that flying these two flags will help people compare the designs and decide their favourite for the referendum.
"For the duration of the second referendum, Auckland Airport will also fly the current New Zealand flag and the proposed silver fern alternative from the four smaller flag poles above our international terminal building."
In accordance with official flag protocol, the current New Zealand flag is flying above the proposed alternative silver fern flag on the airport's main flag pole.
The two flags were raised just after midnight and will fly until March 24, when the referendum ends.
The flags being used by Auckland Airport during the second referendum have been supplied by the Flag Consideration Project.