"We did not want to have to deal with more refugees because we already have enough problems with refugees in Chad," he told a press conference at the UN in New York.
The Austrian soldiers comprise 49 regular troops and about 20 special forces members.
Eufor has a UN mandate to provide security for refugee camps sheltering more than 400,000 people in eastern Chad.
The deployment of the force was delayed earlier this month after an armed opposition alliance launched an attack on the capital Ndjamena in an attempt to topple Idriss Deby, Chad's president.
Major Ortwin Gamener said the Austrian troops were not deterred by the opposition alliance's march on the capital, which was eventually resisted by Chadian government forces.
"Of course these happenings make things a little bit complicated, but we are well informed and well trained and our families have all the information necessary to convince them that things here are not so bad after all," he said.
The Austrian contingent will eventually total up to 140 soldiers and will be deployed in Abeche, an eastern Chadian town.
Abeche is used as a base for humanitarian operations by dozens of UN and other international relief agencies.
French soldiers are on the ground in Ndjamena and Abeche. Irish army soldiers and Swedish special forces are also in the country.
In all, 14 EU nations are contributing to the Eufor force, but more than half of the eventual 3,700 total will come from France.
Spindler, the UNHCR spokesman, said the majority of new refugees crossing into Chad had already been displaced once or twice in Darfur, where Sudanese government forces and local opposition forces have battled since 2003.
"All of them fear going back to Darfur and have asked to be moved further inland into Chad, as they do not feel safe near the border," he said.
He said that UNHCR staff had cited several cases of sexual violence and abuse by fighters against girls and women.
The UN agency said it was also airlifting aid to thousands of Chadians seeking refuge in Cameroon after the opposition alliance's attack on Ndjamena in early February.