The SPÖ and the ÖVP have been struggling to respond to the number of asylum requests, which rose above 28,300 between January and June alone - as many as for the whole of 2014. Officials expect the total to reach 80,000 this year.
The federal government has struggled to provide accommodation for people as many local authorities have refused to accept any refugees.
The draft law means communities who haven't yet taken in any asylum seekers will now be obliged to - with the quota set to up to 1.5 percent of the local population.
The coalition had needed the support of the Greens as the legislation requires a change to the constitution, and therefore needs a two thirds majority in parliament.
Heinz Christian-Strache voiced his anger at the quotas on Tuesday, saying that they have been imposed on the Austrian people in an undemocratic manner. “It's monstrous to try and simply push this law which is hostile to the population through parliament,” he said. He is now calling for a petition (Volksbegehren) to be held on the matter.
The draft law still needs to be passed by parliament but is expected to come into force in October.
Human rights lawyer Georg Bürstmayr told the ORF that the legislation is necessary as the federal government is made responsible for human rights issues by European law and "it is not up to the provinces to make decisions about human rights in a democracy".
Amnesty International recently called conditions at Austria's main refugee camp a "disgraceful" violation of human rights. The Traiskirchen camp, 20 kilometres south of Vienna, has had to stop accepting new arrivals because of disastrous sanitary conditions and hopeless overcrowding.
Built to house 1,800 people, the camp and an adjacent government building are currently home to 4,000 men, women and children.