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Mr Key is scheduled to leave for Washington on Thursday evening, when the preliminary vote on the referendum will be revealed by the Electoral Commission.
It is understood he will be taking some time off before attending a Nuclear Security Summit. He will not be in the country when a final referendum result is confirmed next week.
Mr Key told reporters at his weekly press conference this afternoon that a flag change remained his "strong preference" but he wanted New Zealanders to embrace whichever flag was chosen and to wear it more proudly.
Asked whether the alternative flag, a silver fern design, could become a secondary national flag, he said this was unlikely.
"I wouldn't have thought so. I think if the country votes for the existing flag we will go back to the situation we had before."
Recent polls showed that while the Kyle Lockwood-designed flag was gaining support, the existing flag is still the overwhelming favourite to win the referendum.
In the event that the flag did change, Mr Key said it would cost around $2.7 million to switch to the new design.
This was the price of changing 1500 flags on public buildings around the country. The estimate did not take into account several other costs including changes to police uniforms and Royal New Zealand Navy ships.
Any required changes to passports or driver licences would take place when they were renewed, and no documents would be recalled.
Nearly 1.8 million people, or 56 per cent of voters, have now voted in the second referendum.
In the first referendum, a run-off between five alternative flags, 1.55 million people voted.