0Prime Minister Viktor Orban paid a snap visit to the border late Monday to check on progress, later telling an online newspaper that he was convinced "the works in progress have to be sped up".
"Everyone has to get ready to do intensive work in the coming weeks," Orban said in an interview with the Magyar Idok website published today.
Hungary's border with Serbia has become a major crossing point into the European Union, with more than 160,000 entering Hungary so far this year including 2,706 on Monday alone, police said.
A razor-wire barrier along the 175-kilometre (110-mile) frontier was completed on August 29, but has failed to stop large numbers of people climbing over or under it.
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Hungary is therefore building an additional fence four metres (13 feet) high despite widespread criticism, with France's foreign minister saying the barrier does "not respect European values".
Late yesterday Csaba Hende resigned as defence minister after a meeting of the National Security Council to review progress on the fence.
"Csaba Hende's resignation was in connection with that," he added.
Kosa said the deadline for the fence's completion remained "the end of October, beginning of November" and that the fence would be continually strengthened and developed.
Hende's replacement as defence minister said meanwhile Tuesday that the fence was a "top priority".
"The necessary manpower and technical conditions will be provided to finish the fence," Istvan Simicsko said after a meeting of a parliamentary military and security committee.