But the invitation is good for whoever is president, Mr Lavrov made clear yesterday.
Prime Minister Vladimir Putin is expected to return to the presidency for a third term.
The free trade agreement being negotiated between Russia and New Zealand is scheduled to be signed at Apec when New Zealand would have achieved two historic firsts: the first developed country to get an FTA with China and then Russia (plus its customs union partners Belarus and Kazakhstan).
Negotiations have been delayed because Russian trade officials have been diverted into getting accession to the World Trade Organisation, which was confirmed in December.
Mr Lavrov said signing an FTA with New Zealand would be a "symbolic event".
"It may lay a foundation for similar agreements with countries of the region in the future," he said through a translator.
Mr Lavrov's was the first bilateral visit by a Russia foreign minister - Igor Ivanov attended Apec in Auckland.
Foreign Minister Murray McCully said the bilateral relationship had reached a high point and he described Mr Lavrov at a press conference as one of the world's most experienced and respected diplomatic figures.
Mr Lavrov has been Foreign Minister since 2004, and often chaired the UN Security Council as the former Permanent Representative of Russia to the UN.
Russia has vowed to veto any move by the Security Council to sanction military intervention in Syria and opposes new sanctions against Iran over its nuclear programme.
"Russia has been consistent in its position that sanctions are not going to work and are going to be counter-productive.
"It's the confirmation of the law that every action gives rise to counter-action and these sanctions are going to yield no good."
He is leading the bid to extend Russia's influence in the Pacific and after visiting Australia he will be flying to Fiji to host his second meeting within a year of Pacific foreign ministers and leaders.
Mr Lavrov rejected claims made by Georgia's Prime Minister, Nikoloz Gilauri, and Foreign Minister Grigol Vashadze, that Russia was buying support in the Pacific, by funding countries (Nauru and Tuvalu) that recognised breakaway territories from Georgia, South Ossetia and Abkhazia.