BRUSSELS – The German government backed a $1 trillion rescue package for Europe’s troubled currency union as European Union officials readied tougher oversight over budgets and economies of most member countries in an effort to contain the region’s troubling debt crisis.

The startling size of the EU package, agreed early Monday, initially lifted the euro and stock markets, but by Tuesday the euphoria had ebbed on concerns that simply making more loans available didn’t address the crippling levels of government debt in countries such as Greece and Portugal.

The euro slipped to $1.2670 in European trading — down from $1.2804 in New York late Monday.

Germany, Europe’s richest nation which only reluctantly backed the deal, has demanded that Greece and other countries that use the euro must make sharp spending cuts to curb runaway deficits and public debt in return for financial help.

The Greek debt crisis has become Germany’s burden because Berlin will provide the largest chunk of the eurozone rescue package available to all countries if they need it — at least euro123 billion — and a separate bailout for Greece agreed earlier which did little to halt the crisis. Germany’s share of that is euro22.3 billion.

The idea of shouldering the debts of less thrifty countries is unpopular with frugal German voters who showed their disapproval of Chancelor Angela Merkel by voting her party out of power in a key state election on Sunday.

The German parliament will now need to debate and vote by June 4 on the eurozone rescue. Opposition lawmakers voiced dissatisfaction over the package, which troubles even some of Merkel’s own advisors.

Merkel has tried to couple her backing of the unprecedented bailouts for spendthrift eurozone nations with calls for them to shape up their finances — or ship out of the euro.

The EU’s executive commission will lay out the first step toward stricter budget controls on Wednesday when it will overhaul existing EU rules intended to prevent debt troubles.

EU Commission President Jose Manuel Barroso has called for EU oversight to go further and monitor how EU economies are performing.

“We cannot have a monetary union without an economic union,” he said Monday.

“The solution of this problem has been more coordinated Europe, more coherence, economic policy coordination.”