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(CNN) -- India's external affairs minister says he plans to talk with U.S. Secretary of State John Kerry on Thursday in an effort to defuse a public spat over the treatment of an Indian diplomat who was arrested in New York last week.

The arrest and strip-search of Devyani Khobragade, India's deputy consul general in New York, by U.S. authorities on charges of visa fraud related to her treatment of her housekeeper has provoked uproar in India.

Prime Minister Manmohan Singh has called the diplomat's treatment "deplorable." And Indian authorities have carried out numerous measures to express their displeasure, including the removal of security barriers from outside the U.S. Embassy in New Delhi.

The delicate, complex case has put an unexpected strain on relations between the United States and one of its main Asian allies.

"In terms of our relationship with the United States, I do feel this must be resolved," Indian External Affairs Minister Salman Khurshid said as he announced his intention to talk to Kerry, according to CNN sister network IBN.

Dispute over treatment

Kerry expressed regret over the situation in a call Wednesday to Indian National Security Adviser Shiv Shankar Menon, who has described the treatment of Khobragade as "barbaric."

But U.S. law enforcement officials have defended the way the case has been handled, noting that strip-searches are part of standard procedure in the processing of defendants.

U.S. Attorney Preet Bharara, the prosecutor in the case, said Wednesday that Khobragade, 39, received better treatment during her arrest on December 12 than most American defendants.

He said the outrage in India has drawn attention away from the serious charges against Khobragade, which carry maximum sentences of five to 10 years in prison. Prosecutors say she lied to U.S. authorities about the salary and working hours of her housekeeper, Sangeeta Richard, who is also an Indian citizen, paying her far less than stated in her visa application.

Khobragade's lawyer, Daniel Arshack, denies the allegations, saying the Indian diplomat "did nothing wrong" and claiming U.S. authorities have "made a whole series of spectacular blunders." He says Richard was paid "well above the minimum wage" and that a portion of her salary was being sent back each month to her husband in India.

Many more aspects of the case are in dispute between the different lawyers and government officials involved, including what level of immunity Khobragade is entitled to, the circumstances of her arrest and Richard's actions during her employment.

Calls for an apology

It remained unclear Thursday whether Kerry and Khurshid would be able to find a way out of the diplomatic tangle.

Kerry's expression of regret featured prominently on the front page of leading Indian newspapers Thursday. Commentators and government officials debated whether his comments went far enough.

"An apology from America, acceptance of their fault is what we will be satisfied with," Parliamentary Affairs Minister Kamal Nath said, according to IBN.

As the dispute over her case plays out in public, Khobragade has been moved to India's Permanent Mission to the United Nations, where she may get full diplomatic immunity, Indian officials say.

Richard, meanwhile, has no passport, is living with friends and has been granted temporary legal status that allows her to remain and work in the United States until the matter is resolved, her lawyer Dana Sussman said.

Human rights advocates say the allegations against Khobragade highlight the exploitation of domestic workers around the world.

"It's a good sign that authorities are showing they can take mistreatment of domestic workers seriously," Nisha Varia of Human Rights Watch said in a blog post Tuesday. "It sends the message that no employer is above the law."

CNN's Tom Watkins, Josh Levs, Deborah Feyerick, Elise Labott, Harmeet Shah Singh and Susan Candiotti contributed to this report.