The 48-year-old visitor was at the historical monument on 26 December where he was tested for coronavirus at the gate by a team of health workers. Upon testing positive for the virus in the antigen test, the tourist was barred from entering the Taj Mahal's premises.
The Argentine man has since been untraceable and provided false details, including his contact number, according to Agra district chief medical officer AK Srivastava.
The mobile number provided by the tourist was traced back to Punjab state and there was no hotel by the name his guide mentioned, he said.
Authorities have asked the Archaeological Survey of India to provide surveillance footage from the entrance gate of the Taj Mahal in an effort to identify the man.
Hotel owners in Agra will be instructed to have better coordination with tourists visiting from other countries and note their information, the chief medical officer added.
India has been reviewing its Covid policy as it braces for a potential rise in coronavirus cases in the wake of a sudden monumental spike in neighbouring China.
Earlier, a man who returned from China tested positive for the virus at the Taj Mahal on 25 December. He landed in India on 22 December and reached Agra the next day, authorities said.
"The sample has been sent to Lucknow for genome sequencing. Genome sequencing is important because he came from China," Mr Srivastava was quoted by NDTV as saying. "We are trying to trace his contacts."
He added: "The person has not come in contact with many people as he was in his room most of the time since his arrival."
Thousands of hospitals across the country held mock drills on Tuesday to check the preparedness to tackle a fresh wave of cases. "Such exercises would help our operational readiness, help in filling gaps if any and will consequently strengthen our public health response," health minister Manuskh Mandaviya said.
Health officials have asked citizens to mask up and follow “Covid appropriate behaviour” in crowded places in view of the festive season this winter.
According to local reports, the government is likely to make a negative RT-PCR test mandatory for passengers arriving from China, Japan, South Korea, Hong Kong, and Thailand.
India on Thursday recorded 268 cases of coronavirus, taking the tally of active cases to 3,552, according to the federal health ministry data.