Greece extended for a second time on Thursday a deadline for remaining bondholders to accept a debt swap, giving authorities more breathing space to formulate a response to investors who have refused to sign up for the landmark deal.

Greece said it would settle on April 11 the exchange of 20.27 billion euros of debt, equivalent to the 72 percent of bonds issued under foreign law and state enterprise notes signed up for the swap offer.

Remaining holdouts would be given until April 20 to join in, the government said, extending a deadline that had already been moved back once to April 4.

Greece has said it cannot afford to fully pay holdouts and that the swap deal domestic-law bondholders were forced to accept last month is the best available offer.

The government is left with three options to confront those bondholders still resisting - continue to service the bonds, default and trigger litigation or come up with a new offer while ensuring fair treatment for those that accepted the swap.

Authorities have not decided on a course of action, but none of the outcomes would cause the broader bond swap deal - agreed last month with private sector creditors and a prerequisite for keeping the country solvent - to unravel.

Bondholder meetings were held on March 27-29 on 36 bond issues to vote on that offer. Seven of them representing a face value of 2.45 billion euros were adjourned. Their deadline of April 18 was also extended to April 20.

Greece completed the bulk of its bond exchange on March 12, swapping a nominal amount of 177 billion euros ($235 billion) of domestic-law government paper for new securities, inflicting real losses of about 74 percent on private-sector bondholders.

On Thursday about 50 retail bondholders gathered outside the Bank of Greece, the country's central bank, protesting for not being excluded from the writedown.

Known as private sector involvement, the swap was hailed as a success by Athens, allowing it to procure bailout funds from its euro zone partners and the International Monetary Fund and avert bankruptcy. The exchange triggered credit default swaps.

The outcome for those who do not participate will likely set an important precedent in what is Western Europe's first sovereign debt restructuring in decades.

(Reporting by George Georgiopoulos; Editing by John Stonestreet)