The cost of borrowing for Spain, Italy and Belgium increased as worries over the eurozone debt crisis intensified.
The difference between the yield on German government bonds - considered the safest - and yields for those three countries has reached the highest in the euro's 12-year history.
Late on Tuesday ratings agency Standard & Poor's placed Portugal on credit watch over the country's huge debts.
It came after Portugal's central bank warned of the risks facing its banks.
Portugal's banks faced an "intolerable risk" if the government in Lisbon failed to consolidate public finances, the central bank said.
Christine Lagarde, France's finance minister, said that her country and Germany would stand by Portugal and Spain if they needed financial help.
In an interview with the BBC's Hardtalk programme, she declined to speculate on the likelihood that Portugal and Spain would need a bail-out.
'Lost their shirts'
But Ms Lagarde said: "It is correct to put in place the type of [bail-out] arrangements needed... We did it for Greece and Ireland, and it has to be continued."
Asked if Germany's Chancellor Angela Merkel was right to complain that European taxpayers, rather than investors, were taking all the bail-out risks, Ms Lagarde pointed out that "shareholders in Irish banks have lost their shirts".
However, during the same BBC programme, Dick Roche, Irish minister for European affairs, warned against upsetting the financial markets.
The Republic of Ireland needed to raise money from the bond market to pay for its public services, he said. "If you burn the market, the market will come back and hit you in the face," he said.
Finance officials in France and Germany on Monday accused investors of acting irrationally about the threat of financial contagion, in an attempt to calm fears.
Investors' attitude to Portugal and Spain will come under the spotlight later this week as both countries are set to ask the markets for fresh finance.
Portugal will auction 500m euros of government bonds on Wednesday with Spain asking for funds on Thursday.
The mood among investors will not be helped after S&P said that it had put Portugal on credit watch ahead of a possible downgrade of the country's debt.
The Portuguese government may not be doing enough to enact "growth-enhancing reforms", S&P said. Government policies "have done little to boost labor flexibility and productivity."
Jean-Claude Trichet, president of the European Central Bank (ECB), tried to calm nerves in comments to the European Union's parliamentary committee on economic and monetary affairs.
He said that both Greece and Ireland were solvent, insisting that the eurozone economy was "functioning" and had grown by more than expected this year.
Mr Trichet said that "observers are tending to underestimate the determination of the (eurozone) governments and the EU as a whole."
His comment that the eurozone should not be underestimated may spark speculation that the ECB will expand its controversial government bond purchase scheme.
The ECB has spent 67bn euros (£56bn) on purchases so far.
The rate of return - or yield - on Spain's 10-year bonds jumped as high as 5.7% on Tuesday, a record difference of 3.05 percentage points compared with the benchmark Germany 10-year bond. It later fell back to 5.53%.
Yields on Italian government debt were 2.1 percentage points higher than that on German debt.
Ten-year Irish yields stood at 9.53%, and Portuguese bond yields were at 7.05%.
Meanwhile the euro continued its decline against the dollar to touch an 11-week low.
The euro dropped to $1.2969, its lowest since 15 September, before recovering to $1.2979, down 1.1%. And against sterling one euro was worth 84 pence.
Worries remain about the strength of the weaker members of the 16-country eurozone currency bloc with Spain and Portugal - long seen as the most likely candidates to need outside financial help - joined by Italy and Belgium on the less-favoured list.
Portugal's central bank warned overnight that the country's banks faced an "intolerable risk" if the government in Lisbon failed to consolidate public finances and urged financial institutions to reinforce their capital in the coming years.
Portugal, which approved an austerity budget for 2011 last week, is struggling to meet its targets for deficit reduction.
The German economy, on the other hand, has been very strong this year, with strong demand for exports and falling unemployment.
Hardtalk is broadcast on Tuesday on the News Channel at 2330 GMT in the UK and on BBC World News at 2130 GMT.