Helen Clark's bid for the UN Secretary General job has been raised by Foreign Minister Murray McCully during a meeting with his Russian counterpart in Moscow.
McCully and Russian Foreign Minister Sergey Lavrov also discussed how to turn around a decline in trade over the past two years - despite continuing disagreement over Russia's annexation of Crimea.
The talks are the first visit to Russia by a New Zealand minister since 2014 when Tim Groser was on the brink of concluding a free-trade deal.
Groser was pulled back amid the international uproar over Russia's actions in Crimea.
McCully said he thanked Lavrov for meeting Clark when she visited Moscow recently.
"We fully understand the view that an Eastern European Secretary General should be appointed as a consequence of the rotational process," McCully said.
"New Zealand believes that although this is a relevant consideration, the United Nations today faces very significant challenges to its role and credibility.
"In these difficult times, we believe merit should determine the next person to hold that important office.
"For that reason, New Zealand has nominated Helen Clark, and we appreciated the manner in which she was received in Moscow."
Clark placed sixth out of 12 candidates in a first straw poll and seventh of 11 in a second. The next ballot is on August 29.
Portugal's former prime minister Antonio Guterres led both polls. This week outgoing Secretary General Ban Ki-moon said he hoped the job would go to a woman when his successor was confirmed later this year.
Trade between New Zealand and Russia has declined after Russia seized Crimea in March 2014.
The war of words between Russia and Ukraine intensified this week following Moscow's accusation that Kiev plotted a sabotage attack in Crimea.
McCully said New Zealand and Russia held different views on the situation in Ukraine.
"While we are not part of the sanctions or counter-sanctions process, these differences have constrained trade relations.
"We have discussed how we can improve trade outcomes within the current policy settings."
McCully also expressed New Zealand's appreciation of Russia's intention to send a ship to the New Zealand Navy's 75th anniversary celebrations in November.
The US has also accepted an invitation to send a ship - the first such visit since New Zealand passed its anti-nuclear legislation in 1987.
McCully will have meetings with Britain and France during his trip, which is being made ahead of New Zealand's chairmanship of the UN Security Council next month.
New Zealand is nearing the end of its two-year term on the Security Council and next month's chairmanship will be its second stint.
McCully said he and Lavrov discussed the Syrian situation and New Zealand expressed support for the dialogue between the US and Russia.
"I have urged Minister Lavrov to use Russia's very significant influence to broker a resolution."
McCully's trip to London will be his first official meeting with new British Foreign Secretary Boris Johnson since the UK voted in June to leave the European Union.
He will visit Paris to meet with Foreign Minister Jean-March Ayrault and Hungary for talks with Foreign Minister Peter Szijjarto.
McCully will also be going to Slovakia, which currently holds the six-month presidency of the European Union.
Slovakian Foreign Minister Miroslav Lajcak, who will host McCully, is one of the candidates for the UN Secretary General's position.