"The king accepted the resignation and asked the government to continue in a caretaker capacity," the statement said.
The Flemish separatist New Flemish Alliance (N-VA) won 32 percent of yesterday's vote in the language-divided country, making it the largest party in its Flanders heartland and in the country as a whole.
In line with the country's traditions, King Philip is therefore expected to ask De Wever to try to put together a governing coalition.
Though De Wever's triumph was larger than expected, the French language press Monday dubbed it "an incomplete triumph" and a "non-guaranteed win", while Flemish papers called it a Pyrrhic victory.
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This is because the conservative separatist leader ultimately bent on taking Flanders out of Belgium has no natural allies in the mainstream parties.
Di Rupo's Socialists garnered around 30 per cent in southern French-speaking region of Wallonia, but when combined with the votes of a small sister Socialist party in Flanders are almost neck-and-neck with the N-VA.
Belgium's world-record political impasse ended with the swearing-in of Di Rupo's coalition government in 2011, based on three parties from the north and three from the south.
This time around De Wever, who was hugely acclaimed by supporters, said, "We don't want a long political crisis ... we want to take the initiative to see what is possible.