Kurz began his trip across the Balkans in Bosnia on Monday, before visiting Serbia, Montenegro and Albania discussing the migration crisis with politicians in the region. His trip will finish in Macedonia on Friday.
"If we just stopped refugees at our border, there would really be pressure on the West Balkans," Kurz said on Monday at a press conference with his Bosnian counterpart Igor Crnadak.
Kurz said that Austria wanted to find a common solution with Balkan countries, particularly those like Serbia and Macedonia which are popular migration routes.
"We don't want to put a burden on anyone that he can't shoulder."
"We will protect our border with Macedonia if necessary," Vucic said.
On Wednesday Kurz was asked at a press conference in Podgorica whether Montenegro was threatened by the prospect of Austria closing its borders.
He replied that while Montenegro so far was not on a migration route, such a move would have consequences for the whole region, because "there is a possibility that countries that so far have not been, become a part of the transit route."
His Montenegrin counterpart Igor Luksic told the press that Podgorica had made preparations in the event of Austria putting in place border controls and that it would take appropriate measures in line with the rest of the governments of the region.
Austria took 90,000 asylum seekers in 2015, and announced last month that it wants to limit the number it takes in 2016 to 37,500. Up to 2019, the government says it will accept a maximum of 127,500.
Müssen,um Flüchtlingsstrom zu reduzieren,europ. Grenzen ordentlich sichern&Kooperation mit Balkanstaaten verstärken!https://t.co/v6m2ZPkLJY— Sebastian Kurz (@sebastiankurz) 5 февраля 2016
'It is necessary to reduce the flow of refugees to Europe. Secure the borders in an orderly way and strengthen cooperation with Balkan countries,' Kurz tweeted on February 5.
In Tirana on Thursday, Kurz made similar comments after meeting with Albanian Foreign Minister Ditmir Bushati, saying that it was possible that Austria's move could change migration routes.
'Kurz: We are closing our borders and Serbia, Croatia and Montenegro are doing the same,' B92 reported.
"We are following all possible routes that refugees could use," Ditmir Bushati responded to Kurz's warning.