Global stock markets tumbled after Greece's debt was downgraded to "junk" by rating agency Standard & Poor's over concerns that the country may default.
It makes the struggling nation the first eurozone member to have its debt downgraded to junk level.
Portugal's debt was also lowered on fears of "contagion", adding to the markets' rout and a fall in the euro.
Germany immediately said it would not "let Greece fall", and there were signs that an aid package could be increased.
Greece wants 40bn euros (£34bn) from eurozone governments and the International Monetary Fund (IMF) to shore up its finances.
But there are fears it will not meet conditions needed to access the funds it needs to make looming debt repayments.
When ratings agencies downgrade the country's credit rating - it means they think it is now a riskier place to invest. If it reaches junk status, a country loses its investment grade status. Some financial institutions have rules prohibiting them from investing in "junk" bonds.
Greece's 2-year government bond yield surged to almost 15% on Tuesday, making it highly expensive for the country to borrow from the debt market.
Greek 5-year yields hit 10.6%, higher than many emerging market economies, including Ecuador at 10.5% and Ukraine at 7.1%.
The 2-year Portuguese bond yield jumped to 5.23% from 4.16%.
S&P said it was lowering its rating on Greece's debt to BB+ from BBB-. It also reducing Portugal's debt rating by two notches to A- as doubts intensified about countries with substantial debt relative to GDP.
Greece's finance ministry said in a statement that the downgrade "does not correspond with the real data of the Greek economy."
Portugal's finance minister, Fernando Teixeira dos Santos, also hit back, denouncing an "attack from the markets".
In a statement he described the downgrade and reaction from the markets as "a decisive moment".
"We must remain calm and bring serenity back to the markets," he said. "As in the past, we will do what is necessary to reduce the deficit and promote the competitiveness of the Portuguese economy."
News of the downgrades rocked markets in Europe and the US.
In London, the FTSE 100 index closed down 2.6% with most of the losses following S&P's downgrade of Greece.
Germany's Dax index slid 2.7% and the French Cac-40 lost 3.8%.
On Wall Street, the Dow Jones index closed down 213 points, or 2% at 10,991.
Meanwhile shares in Greek banks slumped by more than 9%, the largest one-day fall in bank shares for 18 months.
Despite earlier hesitation, German Chancellor Angela Merkel on Monday pledged German support to a European financial aid package for Greece, provided "certain conditions" were met.
Germany could provide Greece with up to 8.4bn euros in loans this year. But German public opinion is deeply opposed to the bailout.
In an interview to be published on Wednesday in the business newspaper Handelsblatt, Germany's finance minister says his country will not abandon Greece.
Wolfgang Schaeuble said: "We now have to realise and implement the rescue plan... and thus send a clear signal that we will not let Greece fall.
"We are putting on pressure for quick decisions," he said.
Meanwhile, the Financial Times reported that the International Monetary Fund is considering raising its contribution to the bail-out by 10bn euros to 25bn euros.
Greece needs to raise 9bn euros by 19 May, but has said it cannot go to the markets because of "prohibitive" interest rates.
The Greek government's cost of borrowing on the money markets has reached record levels in recent days amid investor concern over whether a 40bn euro bail-out package will be agreed.
Eurozone countries, together with the International Monetary Fund, have yet to agree details of the package.
Investors are also concerned that the Greek government's austerity measures - designed to cut domestic spending and reduce its ballooning budget deficit - will prove highly unpopular with the Greek public.
S&P warned holders of Greek debt that they only had an "average chance" of between 30% and 50% of getting their money back in the event of a debt restructuring or default.
It said its action to cut the rating resulted from its "updated assessment of the political, economic and budgetary challenges that the Greek government faces in its efforts to put the public debt burden onto a sustained downward trajectory".
The agency added Greece's weak long-term growth prospects made it less credit-worthy.