This comes after the CSU, the Bavarian allies of German Chancellor Angela Merkel's party, announced it is preparing a “seven-point emergency programme” including reinstating border controls with Austria to limit the number of refugees entering Germany from the south.
Bavaria's state premier Horst Seehofer wants to “suspend” the Schengen agreement, which guarantees freedom of movement and abolished border controls between European countries which have signed up to it, at the state's border with Austria.
However, Austria's Interior Minister Johanna Mikl-Leitner (ÖVP) has said that she is against the idea as it would have a negative impact on tourism. She is in favour of EU member states agreeing on a quota of refugees that they pledge to take in.
Bavaria has become a target for refugees entering Europe through Italy and then heading towards Austria. In July, police in Munich reported a "huge increase" in the number of people arriving illegally at Munich's main train station with 600 arrivals in June and July.
Bavarian government figures show almost 17,000 people applied for asylum last year.
“Italy has clearly violated the Schengen agreement,” Seehofer told Bild on Monday. “If that isn't fixed, Germany must really consider putting a stop to it with border controls.”
But the party's suggestions met with immediate resistance from their allies, Merkel's Christian Democratic Union (CDU).
“To tighten borders would be a sign of powerlessness and a confession that the authorities in Germany don't work fast enough,” said Peter Hauk, leader of the CDU group in the Baden-Württemberg state parliament.
Germany was recently praised by the UN High Commissioner for Refugees who called Germany's refugee policy "an example for other European countries to follow".
A CSU spokesman contacted by The Local said that renewed border controls were not yet part of party policy, as they first have to be agreed at a party board meeting on Monday.
Many towns in Bavaria are complaining that they are now overburdened with asylum seekers and refugees.
Under the Schengen agreement and EU border regulations, refugees are supposed to remain in the country in which they first arrive so that the burden can be shared among member states.
But Italy has been accused of turning a blind eye to the refugees passing through the country so that they don't become a burden on its social security system.
Interior Minister Thomas de Maizière recently promised more support to Italy so that the country can deal with the large numbers of refugees arriving on its shores as EU rules require.