Several states have complained that the kits - which are supposed to test for the presence of antibodies against the coronavirus - are malfunctioning.
India imported almost one million kits from China to ramp up testing.
Several other countries have reported problems with kits from China, but Beijing has denied quality issues.
In a statement last week, China said it attached "great importance to the export of medical products".
What is happening in India?
At least three Indian states have expressed dissatisfaction with the kits, with the northern state of Rajasthan refusing outright to use them.
Officials there said the state only had an accuracy of 5%. They added that they used the kits on patients who they already knew were positive, but the tests had shown a "negative" result.
This prompted the Indian Council of Medical Research (ICMR) to ask all states to pause using the kits for two days until it examined them properly.
However, the ICMR said it had always cautioned against wide use of the rapid testing kits as a primary "diagnostic tool" for Covid-19.
The NDTV news channel quoted an ICMR official as saying that data on antibody tests was "still emerging and its utility is still evolving".
How are the tests supposed to work?
The principle is very simple - the test is based on checking for antibodies for the Covid-19 coronavirus from blood samples.
It has been likened in some cases to a simple "yes/no" pregnancy test.
The idea is that it will be able to tell if people had the virus and developed immunity to it.
The kits had been hailed as a "game-changer" tool to help restart economies across the world and governments ordered them in large amounts from China, in addition to trying to develop their own.
However, they are running into problems in a number of countries, including the US and the UK.
What issues are being faced in other countries?
In the US, the New York Times reported that tests of "frankly dubious quality" have flooded the American market, saying that it has been found that it mistakenly flags some people as having antibodies when they actually don't.
In the UK, scientists have said that the tests have a low sensitivity rate and Health Secretary Matt Hancock told the media that they were "not good enough" as yet.
For now, it seems that the lab tests, which are more complex and time-consuming, are still the only reliable method of testing.