The falls come amid fears that Hungary could be the latest European country to default on its debts.
"The problem seems like a cancerous thing - it's spreading from smaller country to smaller country, and many people are afraid that it will spread to a big country like France or Germany, although that's unlikely," Jackson Wong, vice president at Tanrich Securities in Hong Kong, told the Associated Press.
Weak US employment figures released on Friday added to investor worries.
According to the US government's May jobs report, the US economy created 432,000 jobs last month - far fewer than the expected 513,000, with most new posts being temporary hiring by the government for this year's US census.
The Dow Jones industrial average closed on Friday down by more than three per cent as the poor figures dented optimism that a US recovery might offset any further fallout from the European sovereign debt crisis.
In Hungary meanwhile officials spent the weekend racing to play down earlier statements warning that the country was at risk of a Greek-style fiscal crisis.
"The Hungarian economy has healthy foundations and the deficit target of 3.8 percent of gross domestic product can be maintained for 2010 if we adopt certain measures," Mihaly Varga, Hungary's secretary of state and a top aide to Viktor Orban, the prime minister, told reporters on Saturday.
The statement came after Lajos Kosa, vice president of Orban's centre-right Fidesz party, warned last week that Hungary's economic situation was "very critical, the state is comparable to that of Greece".
He added: "The bankruptcy of the state is close."
The remarks sent the Hungarian currency, the forint, and the Budapest stock exchange plunging on Friday.
Although Hungary is a member of the European Union, it retains its own currency rather than the euro.
Varga said the government would be meeting in a special session over the weekend this weekend and would announce various measures on Monday.