Croatian police say that over 13,000 refugees have entered the country from Serbia since the first groups started arriving more than two days ago.
"Are they not more economic migrants because of the sort of structure of the people that are coming through," said Janet Tuskan who's chairperson of the Anglican Chaplaincy in Zagreb.
"Their whole attitude that they're just going to Germany....they don't want to stop anywhere else; they don't give the impression that they're in desperate need, " she added.
Croatian prime minister Zoran Milanovic says his country cannot and will not close its borders to migrants, and is transporting people to Hungary and Slovenia and further towards western Europe.
Most of them want to move on towards Germany or the Scandinavian countries. The Croatian position has sparked anger from Serbia, Hungary and Slovenia.
Croatian authorities say the situation is worst in the eastern town of Beli Manastir, where thousands of refugees have converged and caught local authorities unprepared.
About 2,000 people also gathered in the border town of Tovarnik waiting for bus or train rides to refugee centres in the capital Zagreb and elsewhere.
Many Croatians have been seen trying to help the refugees, with offers of aid and assistance, but most are said to expect the refugees to move on because of a lack of jobs in Croatia.
"People are really very active, spending money buying things. Lots of people I know have gone to places where the people are collecting on the borders or here in Zagreb, said Janet Tuskan who also runs a charity shop in the capital.
UNHCR says more than 442,440 people have crossed the Mediterranean Sea to Europe this year, and 2,921 have died trying.
Listen to Janet Tuskan, chairperson of the Anglican Chaplaincy in Zagreb speaking to Premier's Hannah Tooley on the News Hour:
