The roots of the economic crises in Greece, Ireland and Portugal were distinct, but the countries’ problems shared a common feature: In each, the financial fortunes of the government and the banking system were intertwined, and as one staggered, the other began to falter as well.

Early in the European crisis, analysts and organizations such as the International Monetary Fund recognized that the banks and governments in the euro zone were joined at the hip. Banks are heavy investors in government bonds, and governments provide the ultimate guarantees for the financial system. The two systems rise and fall together.

Untying what the IMF has called a “Gordian knot” has so far proved impossible, increasing the risk that the euro zone’s domino-like run of bailouts will continue.

The renewed sense of crisis has prompted senior officials in the United States and elsewhere to increase the pressure on European leaders for faster action ahead of a summit this month.

The finance ministers of top economic nations conferred by phone Tuesday, and a White House spokesman said there is a “heightened sense of urgency” over the central issues Europe is facing, particularly in its banking sector.

The cruel dynamic of troubled banks and struggling public finances is now pushing Spain closer to an international rescue. Spain’s problems are also driving Europeans toward a “banking union” for the euro zone — a step that would cut the cord between the region’s banks and its governments.

The aim would be to replace the regulatory approach — 17 euro-zone governments regulating 17 banking systems — with a central authority that would have power over the region’s largest banks. In theory, that would put the combined financial weight of the whole euro region behind any bank rescue and decrease the likelihood that banking problems in any single nation could wreck that country’s finances. European leaders are expected to approve the idea, at least in outline form, by the end of this month.

To cut the perilous ties between banking and government finances, European leaders are also discussing proposals to allow Europe’s bailout fund to be used for direct investments in banks. Now, bailout money must be provided in the form of loans to already indebted governments.

When he unveiled those proposals last week, European Commission President Jose Manuel Barroso said faster integration of financial, budgetary and other powers among the euro nations was the only way for the region to put its crisis to rest and cement the euro’s standing as a global currency.

“If there is no strong European Union, or if there are doubts about stability . . . we run the risk of irrelevance,” Barroso said. “Even our most important member states will not have the weight to compete globally” if major initiatives such as the banking union are not put into place.

The connections between the financial health of banks and the financial health of governments are not unique to the euro. The U.S. government, for example, spent hundreds of billions of dollars propping up the country’s financial system after the collapse of the Wall Street bank Lehman Brothers. Financial crises in Asia and elsewhere have typically required twin rescues of governments and financial systems.

But the symbiosis between banks and governments in the euro region is particularly tight. Failing banks can drag down governments, and government debt crises can drag down banks. Adding to the complexity, the exposure of banks and governments in the euro zone crosses national borders. French and German banks, for example, were among the largest holders of Greek bonds and suffered some of the largest losses when the bonds were reduced in value.

Greece’s economic problems began with government spending but affected the banks when investors lost faith in the country’s credit standing and its bonds fell in value. Greek banks were among the largest holders of those bonds, and when they were forced to write down the value of their holdings it wiped out virtually all of their capital. The bailout provided to Greece by the IMF and other European nations included money to rebuild those capital buffers.

In Ireland, the dynamic played out the other way. Massive bank losses, guaranteed by officials in Dublin, forced the country to seek international help when it became apparent that the government could not borrow enough on its own to repair the financial sector.

Spain is grappling with a similar quandary — how to pay for a rescue of the banking system without ruining the government’s credit standing. The final cost is still being tallied but has been estimated at between $50 billion and $100 billion.

A top Spanish official on Tuesday gave the bluntest indication yet that the country will need outside help.

“The market door is not open for Spain,” Treasury Minister Cristobal Montoro told Madrid’s Onda Cero radio on Tuesday.