Athletes caught using meldonium could avoid a ban after anti-doping chiefs said it was not clear how long it takes the drug to leave the body.
Wada announced in September that it was adding the heart disease medicine to its banned list from 1 January.
Since the start of the year, there have been 172 positive tests.
But numerous athletes have claimed they stopped taking the drug last year, prompting many to question how long the drug can stay in an athlete's system.
"There is currently a lack of clear scientific information on excretion times," the World Anti-Doping Agency (Wada) said in new guidance distributed on Monday.
It said that athletes might be able to show that they "could not have known or suspected" meldonium would still be in their systems having taken it before it was banned.
"In these circumstances, Wada considers that there may be grounds for no fault or negligence on the part of the athlete," added the guidance.
On Wednesday, Wada issued a statement saying the new guidance was "not an amnesty" for athletes and they must still explain to anti-doping authorities how the substance was in their body.
This apparent climbdown has already been celebrated by media outlets in Russia, which has borne the brunt of the scandal so far.
Tennis player Maria Sharapova was the first high-profile athlete to test positive for the Latvian-made drug - in a test taken at the end of January - but since then leading Russian athletes from boxing, skating, swimming and winter sports have all failed tests for meldonium.
In a statement, issued via the official news agency Tass, the Russian Sports Ministry said it "supports and welcomes the decision made by Wada because it has showed a willingness to understand the situation, rather than stick to the rulebook".
This follows recent comments from sports minister Vitaly Mutko that the meldonium crisis would soon be "settled".
Last week, the International Biathlon Union said it would not be ruling on any cases until more was known about excretion rates for meldonium.
Wada's new guidance acknowledges that trace elements of meldonium can remain in the body "for a few months" if somebody has been taking the drug for a sustained period.
Sharapova, for example, says she had been using it to treat a variety of health conditions, under medical advice, for a decade.
Leading sports lawyer Dr Gregory Ioannidis said: "It is evident that further research is required and I welcome Wada's acknowledgement of that."
South African anti-doping expert Professor Ross Tucker said Wada's response "seems reactive".
He added: "Perhaps many of the things they now find themselves on the defence for should probably have been done at the time they considered its banning."
Dr Tom Bassindale, a forensic toxicologist and anti-doping scientist at Sheffield Hallam University, believes Wada may have been too hasty in banning meldonium.
"Wada did not have full information about how meldonium is processed by the body when imposing the ban," he said.
"Originally, it was suggested meldonium would be cleared from the body in a week or two but, with the ever-increasing number of positives, I did become concerned this was not the case and it could be accumulating in the body, much like cannabis does in long-term users."