Last week, Prime Minister Viktor Orban said the Hungarian government would consider on Wednesday formally closing the country’s border to stem the inflow of undocumented migrants.
According to Szijjarto, quoted by the Hungarian government's website, the Interior Ministry was instructed to finish preparatory work for the fence by June 24.
Thousands of migrants are coming to Europe as they flee violence in their home countries in North Africa and the Middle East.
In 2014, Hungary is estimated to have received about 43,000 migrants, of which about 95 percent entered the country from Serbia. In 2012 the number was estimated to be about 2,000.
Hungarian Prime Minister's Office chief Janos Lazar said last week the number this year would be higher since about 54,000 migrants are currently estimated to have in Hungary since January.