European leaders are hoping that the right mix of financial engineering, salesmanship and perhaps a bit of Chinese largesse can help put an end to the threats of government default that have been roiling the continent’s economy.

Their newly redesigned bailout fund, known as the European Financial Stability Facility, is a crucial piece of the emergency rescue program approved this week at a summit of senior government officials.

But there’s a risk. Many analysts already say they’re afraid that the European Financial Stability Facility will prove inadequate and underfunded, and that the new rescue package is at best a stopgap measure until the region’s debt crisis escalates further.

The dangers became clearer Friday when the rate Italy must pay for borrowing money over the long term spiked above 6 percent, a level considered unsustainable for a government. This increase in borrowing costs means investors are worried that Italy, the euro zone’s third-largest economy, could have trouble paying its bills even after the rescue fund has been given more firepower to help cash-strapped governments.

In the plan produced this week after days of marathon negotiations, it will fall to the EFSF to try to keep such elevated borrowing costs from turning into a full-fledged meltdown — in Italy or anywhere else in the euro region.

“If it works, if it functions . . . it costs nothing to Europe,” French President Nicolas Sarkozy told French television in a rare prime-time interview to explain the measures unveiled early morning Thursday.

Also unclear is whether the hefty debt relief being provided to Greece will improve its economic situation — the most precarious in the euro zone. Nor is it clear whether a measure aimed at shoring up Europe’s banks, which are weighed down by troubled government bonds, will prove successful.

Yet the most urgent question may be whether a redesigned rescue fund, envisioned as Europe’s chief firefighting weapon, is up to the task.

The EFSF was approved in May 2010 and has provided bailouts for the heavily indebted governments of Portugal and Ireland. But with Germany insisting that the fund be capped at about $600 billion, it has never been able to come up with the overwhelming financial force advocated by the United States and others as the only way to assure investors that Europe’s debts will be repaid.

Klaus Regling, head of the EFSF, and other European officials will appeal to investors worldwide in an effort to expand the fund’s reach and show it can influence the interest rates of countries as large as Italy.

Regling and other European officials traveled to Beijing this week amid widespread speculation that the Chinese government would be asked to contribute to the fund. Chinese officials welcome the rescue effort approved at the European summit but declined to say whether they would be putting money into the fund.

Officials plan to use two strategies to make sure that governments can continue borrowing money, needed to fund their operations, at affordable interest rates.

Officials will create separate funds that would raise money from international investors to funnel into European bond markets and banks. Prospective investors could be provided various guarantees using the EFSF’s available cash. The program may be run out of the International Monetary Fund, which could oversee it, potentially reassuring investors from emerging markets such as China and Brazil.

A second strategy is to have the EFSF offer a sort of insurance. Investors may be told, for example, that if they put $1 billion into Italy, the fund would absorb the first $200 million of any losses. By limiting the potential losses, the hope is that investors would accept lower interest rates for buying bonds. If the insurance covers 20 percent of each bond, that would allow each dollar of EFSF money to draw $5 into European bond markets.

That multiplier is the reason European officials such as Sarkozy say the EFSF’s impact will be upward of $1.4 trillion.

Much of the fund’s $600 billion is already tied up in loans to troubled countries and perhaps only $250 billion to $300 billion is available for the new firefighting mission, according to analysts.

Details of the EFSF programs are expected to be completed during the next month.

Analysts, already skeptical, have reeled off a list of legal, technical, economic and political hurdles the fund faces. Some think the amount of money involved remains inadequate, and insist that the European Central Bank ultimately will have to stay involved in bond buying and other measures it is hoping to curb.

Others say the fund could create new risks if it strains the finances of economically solid nations such as France. As the second largest euro-zone economy, France is one of the main guarantors of any bonds the EFSF issues, and the country’s AAA credit rating is critical for the facility to borrow at the lowest possible rates.

Increasing the reach of the fund without increasing the money in it “means more risk,” said Daniel Gros, director of the Center for European Policy Studies, a Brussels think tank.

There is also skepticism about whether the insurance proposal will make a difference for interest rates. If investors don’t trust that Italian policies are sound, bond insurance is not likely to matter. That’s because a default by Italy would likely involve losses to bondholders of much greater than 20 percent.

Even more important than the effectiveness of the rescue is whether slow-growing economies can rekindle growth, which could make the debt burdens easier to bear. Despite the intense talks and major new programs, “without growth we will not be able to overcome the current situation,” European Commission President JoséManuel Barroso said.

Birnbaum reported from Berlin.