The private debt relief plan negotiated for Greece might make it impossible for the nation to borrow money for years to come and leave it dependent for that much longer on its neighbors or the International Monetary Fund, the IMF warns in an analysis of the new rescue program.

European officials approved $170 billion in new public loans for Greece on Tuesday as part of a three-year plan to stabilize the nation’s finances and diminish the risk that its problems might do more damage to Europe’s economy.

In Athens on Wednesday, officials pressed ahead with changes to local labor laws and other measures that they must enact before they receive the money. Finance Minister Evangelos Venizelos said that the deal would put to rest fears that his country will pull out, or be kicked out, of the euro currency zone.

“The agreement . . . binds Greece to the euro,” Venizelos said on Greek television. “This is a decisive and irreversible action.”

But any hope that the deal would be an immediate salve for the struggling euro zone quickly evaporated. European markets were down Wednesday as economic data confirmed that the regional economy is slowing, and the Fitch Ratings service downgraded Greece, saying the private debt deal would amount to a Greek default even though it is designed to be “voluntary.”

The IMF analysis, meanwhile, suggested Greece’s neighbors may have to carry the country for much longer than expected as the implications of the private debt plan become clearer.

Private debt relief is a central part of the rescue program. ­Under a deal negotiated over several months, private investors will be asked to trade their Greek bonds for new ones that are worth about half as much but which are backed in part by a European rescue fund meant to make them less risky.

The debt exchange — which the IMF calls the largest such deal in history — is to be carried out in the next few weeks as European officials, the IMF and authorities in Athens put the final touches on the complex rescue plan hammered out in weekend talks. By the time that exchange is complete, nearly all of Greece’s outstanding loans will be in the hands of public institutions, such as the IMF, the European Central Bank or European governments.

Theoretically, during the three years of the rescue plan, Greece will restructure its economy, ­become more competitive and resuscitate economic growth — and be ready to wean itself from IMF and European help by again selling bonds to private buyers.

But with so much owed to governments and other public entities — all of which will take priority when it comes to repayment — private investors may well avoid investing in the country.

“Given the high prospective level and share of senior debt, the prospects for Greece to be able to return to the market in the years following the end of the new program are uncertain and ­require more analysis,” the IMF wrote in a bleak assessment of the new Greek program. “Prolonged financial support . . . may be necessary.”

Loans from the IMF or other public entities are generally treated as superior to those made by private investors. Public officials would not put taxpayers’ money at risk without that sort of protection.

The point was illustrated by the position the European Central Bank took during the Greek negotiations. Although the ECB bought tens of billions of dollars of government bonds to stave off Greece’s crisis, it is not being asked to take losses like other investors. Although it might be able to funnel any profits from its Greek bond investments back to the country, the preferential treatment given the bank has only emphasized that any future investors in Greek debt will be at the end of a long repayment line.

With so much Greek debt now in public hands, “you really don’t want to be a private creditor of Greece,” said Mitu Gulati, a Duke University law professor who has studied the Greek debt restructuring.

An IMF official said Wednesday that the outcome will depend on Greece’s economic performance.

“If Greece has implemented reforms, if we start seeing growth, if markets see that this economy is starting to grow and become robust, then new investors will slowly start coming back,” said the official, who is familiar with the Greek program but not authorized to speak for the record.

The possibility that Greece will remain locked out of international markets even after the current bailout runs its course is just one in a long list of risks that the IMF said make the new program “accident-prone.”

Those risks include what the IMF described as a “fundamental tension” at the heart of Greece’s plight: The spending cuts and other measures meant to improve its public finances have triggered a prolonged recession that has worsened the country’s public ­financial situation.

The plan for private debt relief might have some of the same self-defeating elements, according to the IMF study and other analysts. The debt swap will reduce Greece’s outstanding loans by about $130 billion and lower the interest rate it is paying — a major step toward sustaining the country’s financial situation.

But it will also leave Greece saddled with a reputation as the only country in the euro zone — at least so far — that could not fully repay its lenders.

Greece’s trustworthiness also could be damaged by steps the country must take to comply with the debt reduction plan. The debt swap, while voluntary, needs about 95 percent of existing bondholders to participate to generate the savings counted on under the rescue plan. To ensure the savings are reached, the Greek parliament is expected to approve a law subjecting existing Greek bonds to a “collective action clause” — which means that if a set percentage of bondholders agrees to the swap, the decision will automatically apply even to those who don’t want to participate.

The law might be necessary for the nation to achieve that crucial, near-universal participation. But in doing so, Greece would likely be declared in default — at least of a technical sort. Although that wouldn’t be as disastrous as the sort of disorderly default in which a country simply stops making bond payments, it would still carry a stigma.

The fact that parliament is inserting the collective action clause into existing bonds is “de facto coercive,” in effect changing a contract after it has been signed, Fitch said in its latest downgrade of Greece. The debt plan in general amounts to a “distressed exchange” that would place Greece into “restricted ­default,” the agency said.