The party also condemned the "retaliation" threat made by the US President Donald Trump.
The government's decision came a week after a telephonic conversation between Prime Minister Narendra Modi and Trump, who sought supply of hydroxychloroquine to the US to treat coronavirus infected people.
Trump on Monday said he would be surprised if New Delhi did not relent to the request as it has good relations with Washington and warned India of retaliation if it did not export the anti-malarial drug despite his personal request.
"The statement by US President is unacceptable. But Modi govt has succumbed to the threat by allowing the export. That this happened after an expensive gala was organised for him by Modi, instead of preparing to contain Covid-19, shows how this govt has let down India," said Yechury in a tweet.
Trump had appreciated that India was allowing the supply (of hydroxychloroquine) to come out, but if it did not, "that would be okay, but of course, there may be retaliation, why wouldn't there be?"
"Trump's threat of retaliation for easing restrictions on export of vital generic drugs including hydroxychloroquine is just arm twisting. Govt's capitulation to this brazen blackmail undermines vital concerns in our battle against #COVID19. Yet another surrender to US interests," the Left leader said.
He further said that in the recent past, the government has shown "unplanned fiddling" with the export of all sorts of PPE, N5 surgical masks, gloves, ventilators with a disastrous impact on the safety of our frontline health workers.
"Trump's threat to India is in tune with the obnoxious attempts to secure drugs and other pandemic related maternal and in diverting supplies meant for other countries in pure self interest," he said.
"The polit bureau of the CPI(M) demands that this decision is rescinded in the supreme interest of our people's health and safety, which face a major threat from the pandemic," he said.
On March 25, India banned export of hydroxychloroquine in the midst of views in some quarters that the drug could be used to fight COVID-19. India is the largest exporter of the drug.
It is learnt that high-ranking officials of India and the US were engaged over the issue of supply HCQ to the US by certain Indian companies following telephonic conversation between Modi and Trump and the decision to ease restrictions on export of the drug was result of a process.
The assessment in the government on Trump's comment on "retaliation" is that his response was not pre-meditated and that it was an instantaneous reaction by the US President when put on the spot.
There was indication that the decision to lift the partial ban on the two drugs was taken at a high-level meeting last night. ASG RHL