"We will continue to work closely with Italy and Germany, to warn each other even more actively and take all necessary measures to protect the population as much as possible," Kurz wrote on Twitter.
Earlier in the day, Kurz held a telephone conversation with German Chancellor Angela Merkel and Italian Prime Minister Giuseppe Conte, during which the trio discussed the current epidemic situation.
On Tuesday, Austria's first two cases of coronavirus were detected in the southern state of Tyrol, bordering disease-stricken Italy.
As of Wednesday, COVID-19 has infected 81,000 people worldwide with the death toll now over 2,700. Ever since the coronavirus outbreak started in Italy, several European countries reported first virus cases on their soil, including Switzerland and Croatia.