Refugees International says European countries like Romania and Moldova need support from international partners to ensure they can meet the demand.
Australia has contributed $11 million to the United Nations' refugee agency, but the organisation is calling for almost $3 billion to help those fleeing the war.
Daphne Panayotatos, a senior advocate at Refugees International, said many Ukrainian refugees preferred to remain close to home in the hope they could return.
She warned an escalation in fighting could force another sudden, large displacement of people into bordering countries.
"Australia should expand its financial support to Romania and Moldova," Ms Panayotatos told AAP.
"It is important that the countries where refugees will first go and where they want to stay have the resources needed to accommodate them."
Australia promised to grant temporary visas to 9000 Ukrainian nationals, but they only had until July 31 to accept the offer.
Ms Panayotatos said that pushed people into more complicated pathways, instead needing to apply for permanent protection or bridging visas.
"Bridging visas leave people without access to settlement services and cash assistance which are crucial, especially for the single Ukrainian women who make up a large proportion of this population," she said.
Refugees International has called on the international community to help the countries resettling Ukraine evacuees, noting they need support to meet their own commitment on inclusion.
"A broader lesson is the importance and benefits of showing welcome in the form of open borders, regularisation, and early integration," Ms Panayotatos said.
Granting displaced people a broad range of rights, and providing the support required to exercise them, makes refugees less vulnerable to danger and exploitation while promoting their dignity and self-reliance, she said.
13°C