Rahul Gandhi and Shinde Tuesday refused to meet the US Congressional delegation, comprising Republican and Democrat members, to highlight India's strong disapproval of the arrest, handcuffing and strip search of diplomat Devyani Khobragade in New York last week.
US diplomats in consulates have been asked to surrender their IDs, a source told IANS.
On Monday, Lok Sabha Speaker Meira Kumar and National Security Advisor Shivshankar Menon cancelled their meetings separately with the visiting US delegation.
The NSA is known to have described the treatment meted out to Khobragade, India's deputy consul general in New York, as "barbaric" and "despicable", a source told IANS.
Khobragade was strip searched, confined to a cell with drug addicts and also subjected to DNA swabbing, sources confirmed to IANS
Speaker Meira Kumar, herself a former Indian career diplomat, declined to meet the US delegation "as a sign of displeasure" over the treatment meted out Khobragade.
BJP's prime ministerial candidate Narendra Modi too declined to meet the US team. He tweeted: "Refused to meet the visiting USA delegation in solidarity with our nation, protesting ill-treatment meted to our lady diplomat in USA."
Khobragade, one of India's senior diplomats in New York, was charged last week with visa fraud and making false statements.
She was accused by Manhattan's Indian American US Attorney Preet Bharara of visa fraud and exploiting her babysitter and housekeeper. She was handcuffed in public by law enforcement authorities in New York Thursday while she was dropping her daughter at school.
India has termed the treatment meted out to the envoy as "absolutely unacceptable". US Ambassador Nancy Powell was summoned to South Block by Foreign Secretary Sujatha Singh on Dec 13 and a strong protest was lodged over the treatment.
The US delegation is led by Congressmen George Holding (Republican-North Carolina), and comprises Pete Olson (Republican-Texas), David Schweikert (Republican-Arizona), Robert Woodall (Republican-Arizona) and Madeleine Bordallo (Democrat-Guam).