The European Central Bank has kept eurozone interest rates steady at 0.75%.
Mr Draghi said it could only apply to governments of countries that have entered formal programmes with the EU bailout funds.
Market reaction has been negative with stock market falls and the cost of Spanish and Italian debt rising.
Mr Draghi said that the bank is to make detailed preparations to intervene in sovereign bond markets to lower borrowing costs for some eurozone states and to counter investor fears of a eurozone break-up.
He said that the first step had to be taken by governments who had to ask for a formal bailout programme from the rescue funds, the EFSF and ESM.
The ECB may buy up short-term government bonds, which Mr Draghi said would help bring down the cost of long-term borrowing.
Also the ECB is expected to put pressure on governments to carry through reform programmes.
Mr Draghi indicated that the ECB may give up its seniority, or right to be paid back before private bondholders, something that has discouraged private bondholders from investing in weaker eurozone countries.
Mr Draghi ruled out the granting of a banking licence to the ESM, saying it was not currently acceptable under the ECB's rules.
He said the ECB would consider other "non-standard" measures to combat the eurozone crisis, and asserted the euro was here to stay.
He admitted that Germany was the only country opposed to today's moves.