VIENNA (Reuters) - Italy should refrain from sending migrants north towards Austria and Germany or face restrictions on traffic along an important north-south transport corridor, German Interior Minister Thomas de Maiziere said on Tuesday.

Austria, which has mainly acted as a conduit into Germany for migrants who have flocked to Europe since last autumn, also played a leading role in effectively closing the main migrant route into Europe, through the Balkans from Greece.

With warm weather returning to the continent, Austria is preparing for the arrival of more migrants taking another route - traveling up Italy after having crossed the Mediterranean from North African countries such as Libya.

Vienna has said it is preparing to introduce tighter border controls if necessary at the Brenner crossing, an important gateway for goods flowing between Italy and northern European countries such as Germany.

"Italy cannot depend on Brenner always staying open," de Maiziere told ORF television during a visit to Austria to meet his counterparts from other German-speaking countries, adding that Rome could not "as in the past simply guide people north".

Austria has said that tighter controls, such as vehicle checks and crowd-control measures including barriers and a fence like those at its main crossing with Slovenia, will be introduced at Brenner if the number of arrivals requires it.

"We hope that it will not have to be necessary to decide on such matters," de Maiziere told ORF, an Austrian broadcaster. He added, however, that it would also depend on Italy's behavior.

"That is assuming that the numbers coming to Italy are not too high. That is assuming that Italy fulfils its obligations," he said, adding that he had been briefed on Austria's plans.

An Austrian Interior Ministry spokesman said on Tuesday the number of migrants crossing Austria on their way to Germany had fallen to zero. De Maiziere said recently it had fallen to about 140 a day in March, compared to thousands just a few months ago.

De Maiziere said that if the number of arrivals stayed low, Germany would scrap border controls that have held up traffic and angered many people who travel to Germany from Austria.

"According to the current estimate, if the numbers remain this low, we would not continue border controls beyond May 12," he said, adding that Germany still wanted to be prepared for a possible change in the trend.

(Reporting by Francois Murphy; Editing by James Dalgleish)