The news came as the yield on traded Spanish government bonds rose above 6% for the first time since August.
And official figures from Eurostat showed eurozone industrial production for September down 2% from August.
European markets reacted with uncertainty to the news, with the FTSE down by around 0.5% in early afternoon.
Italy sold 3bn euros ($4.2bn, £2.6bn) of 5-year bonds at a 6.29% yield on Monday.
Spanish debt is trading at its highest level since the European Central Bank intervened to cut the cost of borrowing in August.
A high yield indicates investors may not have confidence in the government to fully repay its debts.
The yield on existing Italian debt, traded in the market, topped 7% last week before falling back, after parliament passed new austerity measures and Prime Minister Berlusconi resigned.
High interest rates – or yields – become a problem for the government if it is forced to pay them when it issues new debt.
Monday’s 6.29% rate on new debt is the highest Italy has had to pay since 1997.
It compares with a rate of 5.32% at a similar auction in October.
Spain did not issue any debt on Monday but its government will be concerned by the rising
Investors are looking to see if Italy can form a new government under the leadership of economist Mario Monti.
Around 200bn euros worth of Italian debt will need to be refinanced by April next year.
The September fall in industrial production in the eurozone was not as bad as some investors had feared.
However, production in September increased by 2.2% year-on-year in the eurozone, which was below expectations of a 3.3% rise.
“Eurozone manufacturers are clearly now finding life extremely challenging as domestic demand is hit by tighter fiscal policy across the region,” said Howard Archer from IHS Global Insight.
The eurozone is also being hit by a global downturn.
“Slower global growth has hit foreign demand for eurozone goods hard,” Mr Archer added.
Estonia, Portugal, Italy, the Irish Republic and Germany all saw significant falls in output with German industrial production down 2.9%.
Also, official third-quarter figures for Portugal’s GDP showed a decline of 0.4% for the debt-ridden economy.
The negative economic news dampened the mood on the markets.
By early afternoon on Monday, German, French, British and Italian benchmark indices were all down between 0.5 and 1.5%.
Share values had initially recovered on hopes that changes to the Greek and Italian governments would help resolve the eurozone debt crisis.
However, there are concerns that the eurozone economy could start contracting again by the end of the year.
“The weak end to the quarter suggests that industrial output may contract pretty sharply in Q4,” said Ben May from Capital Economics.
“In all, then, these data appear to support our view that the eurozone will soon fall back into another fairly deep recession.”