Desperate E.U. nations are hunting for coronavirus vaccines — sometimes on a murky open market.

In vaccine-hungry, cash-rich Europe, the hunt for more doses has nations trading with one another, weighing purchases from Russia and China, and fielding offers from middlemen ranging from real to outright frauds.

Amid building anger over a sluggish European Union coronavirus vaccine rollout that has left them far behind several other wealthy countries, many E.U. states are looking beyond the bloc’s joint purchasing strategy, which now seems woefully underwhelming.

An immense black — or at least gray — market has arisen, with pitches from around the world at often exorbitant prices. Sellers have approached E.U. governments with claims of having 460 million doses of vaccines, according to the early results of an investigation by the bloc’s anti-fraud agency that were shared with The New York Times.

While they still plan to get vaccines from the bloc, some nations are also trying to negotiate directly with drug makers and eyeing the murky open market where they are unsure of the sellers and the products. Some have also agreed to swap vaccines with one another, deals some of them now have reason to regret.

The bloc last year was slow to make big advance purchases from drug companies, acting weeks after the United States, Britain and a handful of other countries. This year, the bloc has been blindsided by slower-than-expected vaccine production, and individual countries have fumbled their rollouts.

About 5 percent of the E.U.’s nearly 450 million people have received at least one dose of a vaccine, versus 14 percent in the United States, 27 percent in Britain and 53 percent in Israel, as of this past week, according to databases from Our World in Data and governments.

The stumbles by the world’s richest bloc of nations have turned vaccine politics toxic. Particularly galling to many Europeans is the sight of a former E.U. member — Britain — forging ahead with its vaccination and reopening plans, while E.U. societies remain under lockdown amid a new surge of dangerous variants, their economies sinking deeper into recession.

In the final months of 2020, several countries opted to forgo parts of their population-based shares of E.U.-purchased vaccines. Much of that trade involved less affluent countries, with less infrastructure and hard-to-reach populations, selling their shares of vaccines from Pfizer-BioNTech and Moderna that require ultracold storage, and instead making the cheaper AstraZeneca vaccine, which is easier to handle, the centerpiece of their vaccination campaigns.

But then AstraZeneca, whose vaccine was developed with the University of Oxford, slashed its expected E.U. deliveries because of production problems. And despite experts’ assurances, many Europeans expressed doubts about it after some leaders questioned its efficacy in older age groups, which were not well represented in clinical trials. (Pfizer also suffered a supply slowdown.)

A decision by any country to let go of doses is potential political dynamite, and the recriminations have begun. Poland gave up a chunk of its expensive Moderna quota expected late this year, reasoning that it would not come soon enough to make much difference, considering the country had been anticipating ample deliveries of AstraZeneca and potentially the Johnson & Johnson vaccines by that point.

“I would never give up on buying what is safe and efficient,” said Andrzej Halicki, a Polish member of the European Parliament. “As a former minister, I can tell you that in my view this is criminal action, this is a breach of obligations.”

A German official said the country had secured 50 million Moderna vaccine doses, a significantly larger number than it would get under its population-based allocation of the E.U. supply. E.U. officials confirmed that Germany had obtained at least some of its extra doses from other member states.

Germany also secured a controversial side-deal with Pfizer-BioNTech, for an extra 30 million doses to be delivered later in 2021, prompting anger in parts of the E.U. as the move was seen as the richest E.U. nation leading the bloc to a collective strategy and then hedging by also going at it alone.

The bloc’s fear is that such side-deals could undermine its collective purchasing power and override delivery schedules to all 27 countries.

In a troubling turn, senior government officials and even heads of government have received dozens of unsolicited offers for vaccines. Few of the sellers appear to be legitimate operators, said Ville Itala, director-general of the European Anti-Fraud office, known as OLAF.