(CNN) -- At the request of the government of India, the United States will withdraw one official from its embassy in New Delhi over tensions involving a case surrounding an Indian diplomat.
The decision comes as Devyani Khobragade, whose December arrest and strip search in New York strained ties between New Delhi and Washington, headed back to India.
State Department spokeswoman Jennifer Psaki said she hopes this will help gain closure in the incident.
U.S. prosecutors accuse Khobragade of lying in a visa application about how much she paid her housekeeper. She was indicted this week by a federal grand jury on one count of visa fraud and one count of making false statements.
Her house keeper has also publicly come out to criticize her.
The Indian government denied a request by the State Department to waive Khobragade's diplomatic immunity so she can answer the charges, U.S. and Indian officials said. The immunity was granted after her controversial arrest.
Khobragade arrived at the New Delhi airport Friday, according to an Indian official who is not authorized to speak to the media. The Indian Ministry of External Affairs said earlier in the day that she had left the United States.
Khobragade told CNN, through an intermediary, that the charges against her "are false and baseless."
"I look forward to demonstrating that to all of you," she said through the intermediary.
Khobragade "affirmed her determination to ensure that the episode would not leave a lasting impact on her family, in particular, her children, who are still in the United States," the ministry said.
New Delhi is demanding that Washington apologize and have the charges dropped.
Federal prosecutors allege Khobragade promised in the visa application, under which her housekeeper moved from India to the United States, to pay her at least the minimum wage in New York, and to require she work no more than 40 hours per week.
They allege that Khobragade then had the housekeeper, Sangeeta Richard, sign a second contract, which set her pay her far below the minimum wage and required that she work much longer hours.
"I would like to tell other domestic workers who are suffering as I did -- you have rights and do not let anyone exploit you," Richard said in a statement released Thursday.
Khobragade's lawyers have repeatedly said the diplomat is not guilty and is entitled to diplomatic immunity.
"She is pleased to be returning to her country," her attorney Daniel Arshack said Thursday. "Her head is held high."
Khobragade "did not make any false statements and she paid her domestic worker what she was entitled to be paid," he said.
Richard fled the diplomat's home last summer, and Khobragade started legal proceedings against her and her husband in the Indian courts. Richard has been granted permission to remain in the United States.
Arshack said Khobragade and her legal team were pleased that the State Department had done "the right thing" Thursday by recognizing her diplomatic status.
U.S. officials had previously said Khobragade was entitled to consular immunity, which is less broad than diplomatic immunity and covers only actions carried out under official duties.
Khobragade was India's deputy consul general for political, economic, commercial and women's affairs. But after her arrest, Indian officials appointed her as counselor at the country's permanent mission to the United Nations in New York.
Through that post, she was accorded "the privileges and immunities of a diplomatic envoy," the Indian Ministry of External Affairs said.
Two senior U.S. officials said that the State Department had no choice but to grant Khobragade full diplomatic immunity once she was accredited to the United Nations because she did not pose a national security threat, which is the only reason for which, in very rare cases, immunity is denied.
When India refused the U.S. request to waive the immunity so that she could face the charges against her, she had to leave the country, the officials said.
Khobragade's father, Uttam, thanked people across India for their support in the case.
"Because of the support from all of you ... my daughter is going to come back to her country and unite with the family," he said Friday at a news conference in New Delhi.
He said his daughter had been fighting for the "sovereignty of this country and dignity of the judicial system."
India has expressed outrage over the arrest of Khobragade, who was handcuffed and strip-searched by federal agents on December 12 after a complaint filed by Richard.
Some observers have suggested that Indian officials' protests and repeated demands for an apology are driven by political concerns.
Secretary of State John Kerry expressed "regret" about the situation last month, but stopped short of saying authorities had done anything wrong.
U.S. law enforcement officials have said that Khobragade's strip search was standard procedure and that she received a number of privileges not usually accorded to defendants.
Pressure from New Delhi
Amid the uproar, Indian authorities removed concrete barriers from outside the U.S. Embassy and took away American diplomats' identification cards.
That was followed recently by an order that the United States shut down "commercial activities" at a recreational facility at the U.S. Embassy in New Delhi.
The U.S. Embassy should halt the activities at the property by January 16, an Indian external affairs official said Thursday. The property houses a bowling alley, swimming pool and gym.
The multipurpose club in the embassy compound was used by nondiplomats, Indian officials said, accusing the U.S. of contravening an article of the Vienna Convention.
As the diplomatic fallout deepened, U.S. Energy Secretary Ernest Moniz delayed a trip to India that had been planned for next week.
"We have been in conversation with Indian counterparts about the dates, and we have agreed to hold the dialogue in the near future at a mutually convenient date," an Energy Department official said.
Human rights activists say India's anger about the strip search misses the bigger issue. They say the mistreatment of domestic workers is a widespread and often overlooked problem worldwide.
Officials from both nations have repeatedly said that they hope the issue won't undermine their relations in the long term.
Jethro Mullen reported and wrote from Hong Kong. CNN's Kristina Sgueglia, Elise Labott, Chelsea J. Carter, Harmeet Singh, Faith Karimi and Kevin Liptak contributed to this report.