And the Government was considering further border exemptions for wider family members of Ukrainians in New Zealand.
More than 1.7 million people have fled Ukraine after Russia invaded 13 days ago, according to the United Nations UN.
The UN High Commissioner for Refugees says it is the "fastest-growing refugee crisis in Europe since World War II".
The Act Party has today launched a petition to allow Kiwi-Ukrainians to bring their immediate family to New Zealand as soon as possible.
National last week urged the Government to create a "special humanitarian visa" for immediate family members of Ukrainians who have settled in New Zealand.
The Greens meanwhile want the Government to urgently offer to resettle refugees.
Nataliya Shchetkova, who lives in Auckland with her husband and five children, said most Ukrainians living in New Zealand, about 1500 people, had family in Ukraine who were in increasing danger.
Shchetkova, who moved to New Zealand eight years ago, said her sister-in-law was in Odesa, which was next in line to be attacked by Russia.
"We are so worried, I am scared to call her in case she does not answer."
Shchetkova said a refugee intake of even 500 people would make a huge difference.
"We all have somebody there, people just left in danger. Many don't have help from other countries. They beg us to help and so we are begging the Government to help."
Act foreign affairs spokeswoman Brooke van Velden said she had spoken to many Kiwi-Ukrainians "watching with horror what's happening to their homeland".
"These are people who have parents, brothers, sisters, partners and children caught in the conflict.
"The New Zealand Government has been far too slow to act. The only real things it's done so far is send a tiny amount for some blankets."
New Zealand has so far provided $2 million in humanitarian aid, but so far not announced any measures to help with the flood of displaced people.
"It's time to step up," Van Velden said of the petition.
"The world is uniting against Russian aggression to help the Ukrainian people. The question is what are we doing for our Ukrainian-Kiwi neighbours?
"The Government should allow Kiwi-Ukrainians to bring their immediate family to New Zealand as soon as possible."
On Monday Prime Minister Jacinda Ardern announced a bill to expand sanctions applied on Russia, which would be passed this week under urgency.
So far displaced people from Ukraine have been settling across Europe, with the vast majority in neighbour Poland.
After mounting criticism the United Kingdom is considering widening access to visas for people fleeing the conflict.
The two schemes announced there so far require Ukrainians to either have family in the UK, or a designated UK sponsor. About 50 people had been resettled there thus far.
Home Secretary Priti Patel told the Sun she was looking into "legal options" to grant humanitarian access to people "without ties to the UK".
In 2015 under public pressure the National-led government brought in a specific quota for 250 Syrian refugees escaping the civil war.
New Zealand resettles up to 1500 refugees a year, through the United Nations High Commissioner for Refugees (UNHCR) resettlement programme.
Greens foreign affairs spokeswoman Golriz Ghahraman previously said the Government's response must "focus first and foremost on what we can do to support ordinary people facing crisis".
She said the Government should offer places to 2000 refugees, given the national quota had not been filled for two years, thanks to Covid.
She said Auckland's resettlement centre, where refugees are welcomed into the country, could be used as an MIQ facility.
Ghahraman urged the Government to include refugees from all ethnicities, as well as those from rainbow communities.
