A senior European Union official says a way has been found to get Greece more than $7.6 billion in short-term cash.

Valdis Dombrovskis, the EU Commission's vice president for the euro, said Friday the 28-country bloc has approved $7.6 billion in bridge financing for Greece and that the money will come from funds in the European Financial Stabilisation Mechanism.

In a tweet, Dombrovskis said the money should reach Greece by Monday.

Greece has a $4.6 billion payment due to the European Central Bank on Monday.

Without the so-called bridge financing it would not have been able to make the payment.

Earlier, German lawmakers overwhelmingly backed Friday a new bailout plan for Greece after Chancellor Angela Merkel warned that the cash-strapped country would face chaos without a deal.

Following more than three hours of debate, German lawmakers voted 439-119 in favor of opening detailed discussions on the package. There were 40 abstentions.

The German Parliament's vote capped a week in which the proposed bailout agreed by the 19 eurozone leaders Monday, including Merkel and Greek Prime Minister Alexis Tsipras, has cleared a string of hurdles.

The developments have raised expectations that Greece will secure a financial lifeline to allow the country to get back toward some sort of economic normality following weeks of crisis that's seen banks shuttered for nearly three weeks and withdrawals at ATMs limited to a paltry 60 euros a day.

Germany is one of the few eurozone countries whose parliaments had to approve the step. Earlier Friday, Austrian lawmakers also cleared the way for the talks.

Though the broad outlines of the bailout were agreed Monday, specific terms will now be thrashed out between Greece and its European creditors.

The process is expected to last around four weeks and to lead to Greece getting around $93 billion to help it pay off upcoming debts.

Germany has been the largest single contributor to Greece's bailouts and has taken a hard line, insisting on stringent spending cuts, tax hikes and wide-ranging economic reforms in return.

"The principle ... of responsibility and solidarity that has guided us since the beginning of the European debt crisis marks the entire result from Monday," Merkel told the special session of Parliament.

The alternative to an agreement, she added, "would not be a time-out from the euro that would be orderly ... but predictable chaos."

Merkel will have to return to Parliament to seek approval for the final deal when the negotiations are concluded.

"I know that many have doubts and concerns about whether this road will be successful, about whether Greece will have the strength to take it in the long term, and no one can brush aside these concerns," she said. "But I am firmly convinced of one thing: we would be grossly negligent, even irresponsible, if we did not at least try this road."

On Thursday, the Greek government said banks would reopen Monday for limited transactions, for the first time in three weeks after capital controls were imposed June 29 ahead of a referendum Tsipras called on previous creditor proposals.

Tsipras has acknowledged that the package he signed up to went against his election promises to repeal austerity imposed over the last five years in return for Greece's two international bailouts. But he has insisted he had no other choice, as the alternative would have seen Greece forced out of the euro -- a development that would have further crashed the Greek economy as well as roiling financial markets.