"The validity and reasons for requesting government guarantees have ... not changed but the process has proven to be much more complex and longer than anticipated," the carmaker said in a statement.
"GM's recently improved financial strength has also been a catalyst for making this decision."
GM had wanted €1.8 billion ($2.2 billion) in loan guarantees from European governments including Germany, Britain, where it owns Vauxhall, Spain, Poland, Austria and Belgium.
Germany, home to 23,000 employees, half the European total, last week rejected a request from GM to provide €1.1 billion in guarantees, saying GM has sufficient cash of its own.
With GM's credit rating so weak, having cast-iron government guarantees would have helped it raise money on capital markets much more easily and at lower interest rates.
German Economy Minister Rainer Brüderle responded to the announcement on Wednesday by saying that "GM is making a profit and has the means" to restructure Opel.
"I feel vindicated in my decision" to refuse state guarantees, he told a press briefing. Asked about the risk to German jobs, Brüderle replied that there were "always risks when you make products that do not sell."
GM, which emerged from bankruptcy and posted its first quarterly profit in three years in the first three months of 2010, had been prepared to put €1.9 billion into a restructuring plan, which foresees around 8,000 job cuts.
"We appreciate the support indicated by certain governments, especially the UK and Spain, but we need to move on," GM Europe chief Nick Reilly said in a statement.
"The decision of the German government last week was disappointing and means that the conclusion of these guarantees is again likely to be months away."
GM wanted Germany, home to 23,000 Opel employees, to provide the lion's share of the guarantees, but the German government was annoyed last year by GM's last-minute decision not to sell Opel to Canadian auto parts maker Magna and Russian
"To be clear, our funding needs have not changed and we were led to believe that loan guarantees made available to other European companies under the EU program to help offset the impact of the global economic crisis, would be equally available to Opel/Vauxhall," Reilly said. "But, after a very long process defined by governments, this has turned out not to be the case."
The British government had committed guarantees for €330 million of bank loans and a similar amount had been indicated from Spain.
Germany had been prepared to provide guarantees to Opel if GM sold it to Magna and Sberbank, but GM scrapped the deal in October.
Chancellor Angela Merkel, whose popularity has fallen sharply in recent months, is seen as wary to hand out more taxpayers' money after promising tens of billions of euros in guarantees to prevent a eurozone collapse.