Cabinet will today consider how to help New Zealand-based Ukrainians who want to bring relatives here.
Calls from the community for urgent action are intensifying as Russia's invasion continues.
The National Party has also been urging the government to create a special humanitarian visa for immediate family members of Ukrainians who have settled in New Zealand.
The government has already extended the visas of Ukrainian nationals in New Zealand by 12 months.
It is also allowing Ukrainian nationals overseas with a valid New Zealand visa to enter the country immediately.
Ministers are expected to consider further border exemptions for relatives.
"We are going to consider what we can do to support the Ukrainian community who are here" - Jacinda Ardern
Prime Minister Jacinda Ardern said the UN Refugee Agency (UNHCR) is concerned about countries in the region which are taking in the immediate rush of refugees.
She said that is why UNHCR sees humanitarian support, such as what has already been offered by New Zealand, as so critical.
The UNHCR has not yet asked New Zealand to receive refugees, she said, "but we stand ready when that occurs as well".
Ardern said there are a number of different options to support the wider family of the Ukrainian community who is already in New Zealand.
"We've already extended the visas of those from the Ukraine who are already here for an extra year for anyone who may for instance have had time running out on their visas, we're expediting all visas from Ukrainians who might be seeking to enter and we've also said we're giving priority for entry because ... border restrictions might have delayed that, we've said they can come in immediately."
Further sanctions against Russia
Parliament last week unanimously passed the Russia Sanctions Bill, which allows the government to impose further penalties on those associated with or involved in invasion of Ukraine.
The group of seven ministers given the power to sign off on sanctions will make the first decisions about who will be targeted this week.
But it's unlikely to consider the first tranche today - it can't do this until the Ministry of Foreign Affairs and Trade has developed the regulations.
Ardern has already signalled the first tranche of sanctions will include an extension of the travel ban, restrictions on Russian banks and freezing assets using the existing travel ban list.
More than 100 people are included in the list, including Russian President Vladimir Putin and Foreign Minister Sergey Lavrov.
The second tranche will follow analysis of Russian investment in New Zealand with ties to the invasion in Ukraine.
Through that process, MFAT officials will look at whether more people linked to that investment should face sanctions.
Public records show a handful of wealthy Russians own $60 million worth of land and real estate in New Zealand, including steel magnate Alexander Abramov.
The billionaire owns a country estate in Northland's Helena Bay.