Spain's borrowing costs have risen to their highest level since the launch of the euro, despite a bailout of its banks agreed just days earlier.
The benchmark 10-year bond yield hit 6.81%, the highest since 1999, as optimism about the agreement on Saturday to lend up to €100 billion to recapitalise Spain's banks continued to evaporate.
Italy's 10-year bond yield rose to 6.28%, a rate not seen since January, as concerns about its finances rose.
The BBC reports that the interest rates are seen as unsustainable in the long run for two countries weighed down by huge debts.
Benchmark German 10-year Bunds, considered a safe haven investment, were trading on secondary markets at 1.40% on Tuesday, AFP reports.
Adding to pressure on Spain, ratings agency Fitch on Tuesday downgraded the creditworthiness of 18 of the country's banks, a day after cutting ratings for the two biggest, Santander and BBVA.
Austria's finance minister Maria Fekter on Monday refused to rule out that Italy may need EU rescue money in the coming months, drawing an angry response from Italy's Prime Minister.
Italian Prime Minister Mario Monti said her comments were "completely inappropriate" for an EU finance minister.
On Tuesday, Ms Fekter softened her remarks, emphasising that there were no signs that Rome would need bailout aid.