"This situation gives the possibility to Hungary to improve the country's image abroad," Gergely Gulyas said at a briefing.
The Hungarian government designated Serbia as one of its "safe countries of origin," alongside other former Yugoslav states, in July. The country's amended Asylum Act says those who enter Hungary through what they term a "safe" country will be denied asylum.
Gulyas reaffirmed Budapest’s strict adherence to the new legislation.
Local media reports emerged late Tuesday that refugees passing through Serbia had begun moving toward Croatia.
US Vice President Joe Biden said earlier Washington would consider additional aid in support of Serbia’s "steadfast efforts to cope with an unprecedented refugee and migration crisis."
Hungarian Army Unable to Operate on Border Without Legal Amendment
"Army forces cannot be involved in the protection of the border until the amendment to the law is passed… We hope that this amendment will be adopted on Monday," Gulyas told reporters.
He argued there was "no obstacle" for troop presence at the border and stressed that soldiers would not be allowed to use weapons.
A strict border control package of laws came into force at 22:00 GMT Monday as Hungary documented over 190,000 migrants crossing into the country this year. New crisis legislation from Budapest imposes strict prison sentences for illegal border crossing and damage, including destroying border fences, to state property.
Police intercepted 366 migrants on Tuesday, one day after having rounded up a record-setting 9,380 people in a single day.