The slave labour accusation follows an investigation that found an Indian textile factory supplying goods to the company pays staff just 16p an hour.
War on Want, the charity group, alleges Tesco buys clothes from the Bangalore factory where workers can earn less than £7 a week.
The accusation comes at the same time as an intervention by Obama, who wrote to Tesco chief executive Sir Terry Leahy urging the company to talk with the US grocery workers' union over representation for workers at Fresh & Easy, Tesco's US chain.
War on Want's report will be presented at Tesco's annual general meeting tomorrow by a researcher flown in from India.
It follows last week's news that cut-price fashion retailer Primark sacked three suppliers in India after a BBC Panorama programme found that they were sub-contracting work to companies which used children for embroidery work.
A spokesman for Tesco said: "It's disappointing that War on Want has once again chosen to publicise unsubstantiated allegations without engaging with us.
"We have been trying to discuss our approach to ethical trading with them but they have ignored our calls. Now, out of the blue, they make these allegations without producing any evidence or giving us any detail on the factories they claim have problems. This means we cannot investigate.
"We insist on high standards and go to great lengths to ensure our suppliers meet them."
Obama has become embroiled in the long-running battle between the United Food & Commercial Workers Union and Tesco over union recognition.
Obama wrote in his latest letter: "I again urge you to reconsider your policy of non-engagement in the United States and advise your executives at Fresh & Easy to meet with the UFCW. I am aware of Tesco's reputation in Britain as a partner to unions. I would hope that you would bring those values to your work in America."
The union represents more 1.3m retail workers in the US, where Tesco plans to roll out hundreds of Fresh & Easy stores across California, Arizona and Nevada.
Tesco, which is unionised in the UK and works with Usdaw, said it believed that union membership was a matter of individual choice.
"If our people want to join a union then they can and will. All the signs so far are that there is little interest in doing so," Tesco said.
The UFWC endorsed Obama over Hillary Clinton in the race for the Democratic presidential nomination in February.
Read more about the US general election and Barack Obama's campaign here.