They said that today at 6:00 am (0400 GMT) a total of 34,131 migrants had entered Slovenia since Saturday, when the influx began, compared to 21,455 the previous day, an increase of 12,676.
On September 23, Hungary, which has since closed its borders, counted a record 10,046 arrivals in one day.
Another 10,000 were expected in Slovenia today, as the country of two million people became the latest state to see a surge of refugees desperate to reach northern Europe before winter.
In response to the crisis, the parliament voted early Wednesday to grant greater powers to the army and allow soldiers to join border police in patrolling the 670-kilometre (416-mile) frontier with Croatia.
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Ljubjana also voiced sharp criticism over Zagreb's decision to open its borders on Monday night, letting thousands of people into Slovenia.
The European Union on Wednesday called a mini summit with Balkan countries in Brussels on the migrant crisis.
The continent has been struggling to find a unified response on how to tackle its biggest migration crisis since 1945.