"Last week's surprising Parliament vote in unanimous support for the blatant anti-Russian legal move showed that MPs had long since made up their mind with regard to the situation in Ukraine and hardly need additional advice," he wrote.
"I reiterate, my direct address to support such an important committee hearing would have made perfect sense had it been set up before the vote rather than as a follow up now, that the Russia Sanctions Bill measures are in the pipeline, and the blame-the-Russians public campaign in New Zealand is on the rise."
New Zealand has brought in independent sanctions against Russian oligarchs, officials and their families, as well as a 35 percent tariff on all Russian imports.
Zuev referred the select committee's chair, Labour MP Jenny Salesa, to the embassy's online resources for materials relating to the official Russian stance on the situation in Ukraine, and said the embassy "shall stand ready to provide you with additional materials and clarifications at our disposal".
In response, RNZ understands the committee asked him again to appear, outlining the powers someone has to compel someone to appear, but he did not respond.
It is understood the committee is actively investigating whether Parliament can summons the ambassador, and how far the protections of the Vienna Convention - which guarantees diplomatic immunity - extend.
RNZ has sent repeated requests for the ambassador for an interview, but his office only referred to the letter to Salesa.
Waikato University international law professor Al Gillespie said the ambassador should not be summonsed to appear.
"He should be invited, but not summoned. Such moves are getting close to violating the spirit of the Vienna Convention on Diplomatic Relations," he said.
The convention guarantees diplomatic agents freedom from arrest or detention, immunity from criminal or civil prosecution except in very specific circumstances, and excludes them from obligations to give evidence as a witness.
Gillespie said diplomatic agents were however required to respect the laws and regulations of the receiving state, and had a duty not to interfere with the state's internal affairs, but the way to respond to that would be speaking behind closed doors or - as the heaviest sanction - to designate them persona non-grata.
This would cause Russia to be required to recall their ambassador, or terminate his functions within the embassy.
Gillespie said New Zealand should handle the situation carefully for three main reasons.
"(a) What happens to the Russian ambassador will probably happen to the Kiwi ambassador in Moscow; (b) At some point, this war will end and we will need to rebuild relations, (c) there are other ways to express displeasure - like expelling some junior members of the mission."
Before the invasion in February, Foreign Minister Nanaia Mahuta had already called Zuev in to hear New Zealand's objections to Russia's aggression.
National has been calling for the ambassador to be expelled since shortly after Russia's invasion of Ukraine was launched, saying the time for diplomacy is over.
Prime Minister Jacinda Ardern has refused, saying only one other country had done so, economic sanctions were more effective, and the government wanted to keep consular and diplomatic channels open.
The Green Party has backed that position until now, with foreign affairs spokesperson Golriz Ghahraman saying Zuev should be expelled if he still refused to appear before the committee.
"The job of a diplomat is to continue dialogue, so that's what we honour until he ... honours the same," Ghahraman said.
Ardern has not ruled out removing the ambassador in future.
Last week, after MPs and high-level defence and security personnel were blacklisted for travel to Russia, Gillespie suggested New Zealand could expect further sanctions from Russia including against high-profile individuals.
He said the recent emergence of war crimes and crimes against humanity in the conflict had changed the nature of it.
While at this point removing the ambassador would not be in New Zealand's best interests, the changed nature of the conflict might now warrant sending weapons or considering removal of some lower-level officials from the embassy.