By Aaron Kuriloff 

Investors in Puerto Rico's bonds braced for losses as soon as this week, after the U.S. commonwealth said it can't pay its debts as it works to stave off a cash crunch and rebuild its ailing economy.

The price of some Puerto Rico bonds sold last year touched record lows at about 68 cents on the dollar Monday after the government released a report by former International Monetary Fund officials calling for talks with bondholders about taking losses, including extending the time frame of some debt and lowering payments.

The announcement brought into relief the consequences of long-running financial difficulties on the island, which has about $72 billion in debt outstanding, a greater sum per capita than any U.S. state. Analysts said the central government may run out of cash within a month, which could lead to a government shutdown, employee furloughs and other emergency measures.

In a speech Monday, Gov. Alejandro Garcia Padilla called Puerto Rico's debts "unpayable."

"Let me be clear: This is not about politics. This is about math," he said. "The only way that we can climb out of this mire is if we come together and are willing--bondholders included--to assume shared sacrifices today, so that tomorrow we may all share the benefits of a growing economy."

Many investors stand to lose money, from individuals in mutual funds attracted to Puerto Rico bonds' tax-free status to hedge funds that last year bought more than half of the island's sale of $3.5 billion in junk-rated debt. A group of 35 creditors holding about $4.5 billion in Puerto Rico debt, including Brigade Capital Management LP, Centerbridge Partners LP and Monarch Alternative Capital LP, have proposed financing terms to the government and said in a letter last week that they had been rebuffed. A spokesman for the group declined to comment Monday.

Puerto Rico's move also heightened concerns that the commonwealth's problems could affect the greater $3.7 trillion market for debt sold by U.S. state and local governments. A broad restructuring of Puerto Rico would be a new test for the municipal-bond market amid investor worries about the willingness of distressed governments to repay debt in the wake of Detroit's record bankruptcy. Proceeds from the sale of municipal bonds typically are used to build roads, schools and other public infrastructure.

Meanwhile, a White House spokesman Monday said that the federal government would provide expertise and access to existing resources but no bailout. The administration said Congress should consider legislation introduced last year that would allow the commonwealth's public corporations the same right to seek bankruptcy protection that already exists in the 50 U.S. states.

Even if officials in Washington were willing to reconsider providing some kind of lifeline to the island, "it would come at a significant cost to Puerto Rico," said Sergio Marxuach, policy director at the Center for a New Economy in San Juan, Puerto Rico.

Some Puerto Rico creditors already are facing potential losses. The Puerto Rico Electric Power Authority is in talks with creditors, including banks, bondholders and bond insurers, to avoid default on a $416 million payment due Wednesday. The publicly owned utility has about $9 billion in debt outstanding; it would be one of the largest restructurings in municipal-bond history.

Monday's report also highlighted the breadth of creditor exposure, with even general-obligation bonds, backed not by specific assets but by the government's taxing power, also potentially at risk.

Moody's Investors Service said Monday that the report and recent comments by the governor "suggest a rising probability that the commonwealth will move to restructure the bulk of its bonded debt, even including those that are guarded by the strongest legal protections--primarily the central government's general obligation bonds."

"I think this is a turning point in the strategy from the commonwealth itself," said John Miller, co-head of fixed income at Chicago-based Nuveen Asset Management LLC, which manages about $100 billion in municipal debt, including some from Puerto Rico. "For 20 years now, it's been about protecting market access and borrowing more if there's a gap in the budget.

That strategy became unsustainable about a year ago and was not acknowledged as such perhaps until now."

Gov. Garcia Padilla said: "We must make difficult decisions to meet the challenges we now know are ahead, and I intend to do everything in my power to lead us through this time."

Puerto Rico's problems trace back to the early 1990s, when the U.S. began closing military bases on the island, whose residents have U.S. citizenship but don't pay federal tax on local income. The expiration of corporate tax breaks in 2006 prompted manufacturing and pharmaceutical businesses to leave, putting the island into a deep recession. As the economy worsened, migration to the U.S. mainland accelerated and shrank the island's tax base.

While Puerto Rico's territorial status leaves the commonwealth with few structural tools to fix its debt, the economy itself faces deep challenges, including rampant tax evasion, poor business investment, a bloated welfare state and high unemployment. Puerto Rico's unemployment rate, 12.4% in May, is more than double that of the rate for the 50 U.S. states, at 5.5%

The weak economy has prompted many workers to leave the island in search for better work in the U.S. Puerto Rico's population fell by 5.5% from 2004 to 2013 and was projected to fall another 0.7% last year, which would be the seventh-largest decline in the world, according to a report last year from the Federal Reserve Bank of New York.

"These are problems that built up over decades," Mr. Marxuach said. Many of the island's economic problems, including large unfunded pension liabilities, draw legitimate parallels to Greece, he said, where the Mediterranean country's debt crisis also is escalating. But even Greece has options to restructure its debt and seek emergency assistance from the IMF that isn't available to Puerto Rico. "We don't even have that card," said Mr. Marxuach.

Several analysts criticized the report. Carlos Colon de Armas, a finance professor at the University of Puerto Rico, said the study lacked independent verification of financial data and came to a "predictable but incorrect" conclusion that default or restructuring was the answer. He said Puerto Rico must address bloated public spending, particularly in municipal subsidies and education, to free cash and pay debt.

"What they are going to do is use the report to force bondholders to take a hit," Mr. Colon de Armas said. "It would be a monumental mistake."

Nick Timiraos and Valerie Bauerlein contributed to this article.

Write to Aaron Kuriloff at aaron.kuriloff@wsj.com