Senior politicians in India have brushed aside US attempts to defuse a row over the arrest and strip-search of one of its senior diplomats, with more calls for an official apology.

Tensions between the two countries escalated after Indian deputy consul general Devyani Khobragade was arrested and hand-cuffed a week ago as she dropped her children at school in New York.

While in custody, she was strip-searched and charged with visa fraud and underpaying her nanny, also an Indian national.

In an attempt to resolve the crisis, the US ambassador to New Delhi, Nancy Powell, held talks with senior Indian foreign ministry officials, while top State Department officials spoke with their Indian counterparts for the third time in two days.

The US Secretary of State John Kerry has also expressed "regret" over the incident, saying he hoped that it would not hurt the countries' relationship.

But a senior Indian minister, Parliamentary Affairs Minister Kamal Nath, has warned that India is expecting a full apology rather than expressions of regret.

"They should tender a clear apology. We will not accept this conduct against India under any circumstances," Mr Nath said.

"The US has to understand that the world has changed, times have changed and India has changed. The conduct and attitude that (the) US has shown regarding the Devyani issue is a matter of concern not only for India but also for all countries and everyone should raise their voice," Mr Nath added.

Those demands were echoed by the vice president of the Hindu nationalist opposition Bharatiya Janata Party (BJP), Mukhtar Abbas Naqvi.

"The US will have to apologise," he said.

"This is an extraordinary event and not about the US and India alone. It is an example for the whole world that no diplomat can feel secure in such circumstances."

But the United States is standing firm, refusing to bow to Indian demands to have the charges against Ms Khobragade dropped.

State Department spokeswoman Marie Harf says the US is very clear with the expectations it has for foreign diplomatic staff.

"We very clearly have said... there are obligations they have for their staffs when they bring them to the United States. We make those obligations very clear and we take any allegations that they haven't done so very seriously," she said.

Ms Harf denied that the Government had pressured law enforcement officials to allow Ms Khobragade to be allowed to go free, saying "judicial process is independent" of the government.

"It's not true. The State Department doesn't charge people or drop charges. That's not what the State Department does."

Ms Khobragade has been released on bail of $250,000 after giving up her passport and pleading not guilty to charges that attract a maximum of 15 years in jail.

India is trying to secure full diplomatic immunity for Ms Khobragade, by moving her to its UN mission in New York, but such a move requires State Department approval.

AFP