Mr Kurz has long made tackling immigration a cornerstone of his political life, a position which helped catapult him towards the nation’s leadership in December last year.
And the Austrian Chancellor has repeatedly opposed the EU’s policy of setting up quotas of migrants for each European country to take on, claiming the scheme “isn’t working”.
Speaking from Vienna, Mr Tusk said: “When it comes to managing illegal migration Chancellor Kurz and I have discussed this many times already, and we have similar views.
“It is possible but naturally all sides need to compromise.
“Above all we must put an end to the destructive emotions surrounding the issues of relocation as they continue to fuel populism and divide Europe.
“If the issue is not resolved by ministers within the next month, we will need to find a solution at the June European Council.”
Mr Kurz also pledged to hold an EU summit on immigration later this year when his nation takes on the Presidency of the EU council.
Last month Mr Kurz and Hungary’s Prime Minister Viktor Orban promised to continue their fight against illegal migration after crunch talks in Vienna.
The pair met with a view to forging closer ties in an increasingly divided EU and to discuss border security and the Balkan migration route.
At a press conference after the talks, Mr Kurz said: “We must stop illegal migration in order to ensure safety across the bloc.
“We have to stop illegal immigration in order to ensure security in Europe.
“I am glad that there has been a change in thinking in many European countries in recent years.”
Mr Orban said the “biggest threat” today was the “mass exodus” from other countries into Europe.
He said: “If we want Schengen, we have to close the external borders and open the internal borders, and today we want to open the external borders and close the internal borders.
“When I say that the future needs to be protected I mean that we have a culture, a Christian culture… We have a way of life, and we want to protect this way of life.”