BRUSSELS (AP) -- Private investors agreed Thursday morning to accept losses of 50 percent on their Greek bonds, a European Union official said, removing the last apparent roadblock to a broad plan to solve the continent’s debt crisis.

The deal with private creditors would significantly cut Greece’s debt load, the very problem that kicked off the eurozone’s debt drama almost two years ago.

At an emergency summit in Brussels, European leaders had already agreed to force banks to raise (euro) 106 billion ($148 billion) by June -- partially to ensure they could weather the expected losses on Greek debt.

They also neared agreement on boosting the firepower of the continent’s bailout fund to around (euro) 1 trillion ($1.4 trillion) to help it protect larger economies like Italy and Spain from the sort of market pressures that pushed Greece to need a rescue.

While the breakthrough on Greece, the bailout fund and strengthening the banks was a big success for the eurozone, much of the effectiveness of the plans will depend on the details, which will have to be finalized in the coming days and weeks.

The leaders were under immense pressure to finally get a grip on the eurozone’s escalating debt crisis after multiple delays and half-baked solutions. Market confidence was waning and fears were growing that the crisis could push Europe and much of the developed world back into recession.

But the third prong of their plan -- finding a way to reduce Greece’s crushing debts, which are on track to top 180 percent of economic output -- had been proving difficult, driving leaders, national finance experts and bank representatives to continue talks deep into the night.

German Chancellor Angela Merkel told lawmakers in Berlin that the goal was to bring Greece’s debt down to 120 percent of economic output by 2020.

There were concerns that that would require losses that the banks weren’t willing to take on voluntarily. Having a voluntary deal is important because imposing losses on banks can trigger massive bond insurance payments that risk creating huge turmoil on global financial markets.

A European official said early Thursday that a voluntary deal had been reached.

Another official confirmed that the banks agreed to take losses of 50 percent of their Greek bonds. According to Greece’s debt inspectors that would take the country’s debt to just above 120 percent by 2020.

The officials spoke on condition of anonymity pending an official statement.

A spokesman for the organization that has negotiated on behalf of the banks said he would release a statement soon, without confirming the deal.