The Vermont senator told a TV debate that women "in poor countries" should have access to birth control.
Conservatives said the remark meant the self-described democratic socialist's climate change policy was for fewer "brown babies".
The UN forecasts the Earth's population will rise to 11 billion by 2100.
On social media on Thursday, Mr Sanders was likened to a Marvel movie villain.
Senator Ted Cruz said the Democratic White House hopeful's remarks evoked Thanos, the Avengers baddie who kills half the world's population with a snap of his fingers.
The Texas Republican joked: "In a surprise move, last night Bernie announced Thanos as his running mate."
What did Bernie Sanders say?
The population control issue was raised during a CNN climate town hall event in New York City on Wednesday night during a question from an audience member.
Martha Readyoff, a teacher, said the topic was "poisonous for politicians, but it's crucial to face".
"Empowering women and educating everyone on the need to curb population growth seems a reasonable campaign to enact," she began.
"Would you be courageous enough to discuss this issue and make it a key feature of a plan to address climate catastrophe?"
Mr Sanders, who is running for the Democratic presidential nomination to face President Donald Trump in the November 2020 election, replied: "Well, Martha, the answer is yes.
"The answer has everything to do with the fact that women in the United States of America, by the way, have a right to control their own bodies, and make reproductive decisions.
"The Mexico City Agreement which denies American aid to those organisations around the world that allow women to have abortions or even get involved in birth control to me is totally absurd.
"So I think, especially in poor countries around the world where women do not necessarily want to have large numbers of babies, and where they can have the opportunity through birth control to control the number of kids they have, is something I very, very strongly support."
The Mexico City Policy is a US government rule to ban overseas organisations that receive federal aid from performing abortions, even with other funding.
The measure was rescinded under Democratic President Barack Obama, and reactivated in January 2017 by Mr Trump, a Republican.
What's the other reaction?
US conservative outcry followed the Vermont senator's comments.
Steve Scalise, a Louisiana Republican congressman, tweeted: "Bernie Sanders said YOUR tax dollars should be used to fund abortions in foreign countries to reduce population size."
Conservative writer Liz Wheeler tweeted: "Imagine being so disgusting that you want to force Americans to pay for abortions to kill brown babies in foreign countries so you don't feel guilty flying private jets & visiting communist nations."
CNN host SE Cupp accused Mr Sanders of entertaining the racist ideology of eugenics.
Another conservative commentator, Ben Shapiro, tweeted that Mr Sanders wanted to facilitate abortions for "disproportionately babies of colour, in order to fight climate change".
Amid the backlash, Mr Sanders' Twitter account issued several posts about climate change, though it did not address population control directly.
What's the context?
According to a 2017 study published in the Lancet medical journal, global fertility rates are in decline because individual women are having fewer children.
Even so, the UN forecasts the Earth's population will climb from 7.5 billion now to nearly 10.9 billion by 2100.
Mr Sanders is not the first Democrat to raise population control as a tool for tackling climate change.
In his 1992 book, former US Vice-President Al Gore wrote: "No goal is more crucial to healing the global environment than stabilising human population."
Research indicates that babies in wealthier nations tend to have higher carbon footprints than those in still-developing countries.
According to a World Bank study, for example, Americans produce 16.5 tonnes of carbon dioxide per capita every year.
By comparison, only 0.1 tonnes of the greenhouse gas is generated in Ethiopia per inhabitant.
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