China has denied having any Indian soldiers currently in custody, as both sides try to lower the temperature following a fatal clash along their disputed border in the Galwan Valley.
Indian media had reported that China detained 10 Indian soldiers in the fight, releasing them on Thursday.
Chinese government spokesman Zhao Lijian said on Friday that no Indian soldiers were "currently" being held.
The Indian government said only that none of its soldiers were missing.
The careful wording of the statements did little to clarify whether Chinese forces in the contested area had taken Indian soldiers into custody and subsequently released them.
Indian media reports suggested that a lieutenant-colonel and three majors were among 10 held by the Chinese, and that their release was the top priority in military and diplomatic talks between the nuclear powers on Wednesday.
Asked at a press conference about the reports, Mr Zhao said: "As far as I know, currently, China has not detained any Indian personnel".
The conflicting reports were the latest round of confusion over what exactly happened in the Galwan Valley on Monday.
At least 20 Indian soldiers died in the clash, which was fought without any firearms because of a 1996 agreement barring guns and explosives from the area, and at least 76 Indian soldiers were injured.
China has not released any information about casualties, though India said both sides suffered losses.
The two nations have accused the other of crossing the poorly demarcated border and provoking the fight.
Shiv Aroor, a senior editor at India Today, tweeted on Thursday with what he said were details of the release of the Indian troops.
To those asking, (and since it’s been reported now) — that’s what my tweet below 6 hours ago was meant to convey. And since the story will be in tomorrow’s papers, if you’re interested in hearing about it from me, here you go: https://t.co/xsMJtUWdaW pic.twitter.com/lxfQKb608N— Shiv Aroor (@ShivAroor) June 18, 2020
In his press conference Mr Zhao, acknowldged that the two nations were in communication over diplomatic and military channels. "We hope India can work with China to maintain the long-term development of bilateral relations," he said.
But it was "very clear and the responsibility lies entirely with the Indian side", he added.
The conflicting reports over soldiers in custody came after an image emerged on Thursday purportedly showing some of the crude weapons used in the fight.
The photograph, which appears to show iron rods studded with nails, was passed to the BBC by a senior Indian military official on the India-China border, who said the weapons had been used by the Chinese.
Defence analyst Ajai Shukla, who first tweeted the image, described the use of such weapons as "barbarism". The absence of firearms in the clash dates back to a 1996 agreement between the two sides that guns and explosives be prohibited along the disputed stretch of the border, to deter escalation.
The image was widely shared on Twitter in India, prompting outrage from many social media users. Neither Chinese or Indian officials have commented on it.
Media reports said troops clashed on ridges at a height of nearly 4,300m (14,000 ft) on steep terrain, with some soldiers falling into the fast-flowing Galwan river in sub-zero temperatures.
First deaths in four decades
The two sides have brawled along the disputed border in recent weeks, but Monday's clash was the first to lead to fatalities in at least 45 years. Unconfirmed reports in Indian media said at least 40 Chinese soldiers died, but China is yet to issue any information about casualties.
China on Wednesday claimed "sovereignty over the Galwan Valley region" - a claim rebutted by India as "exaggerated and untenable".
Members of the public in both nations have since staged protests over the clashes in the disputed Himalayan border area, while officials have spoken cautiously and moved towards a diplomatic resolution.
Indian foreign ministry spokesperson Anurag Srivastava said the foreign ministers of both countries had phone conversation on Wednesday on the developments and "agreed that the overall situation should be handled in a responsible manner".
"Making exaggerated and untenable claims is contrary to this understanding," Mr Srivastava was quoted as saying by Press Trust of India news agency.
An Indian government statement after Subrahmanyam Jaishankar's conversation with China's Wang Yi said Chinese forces tried to erect a structure on the Indian side of the de facto border, the Line of Actual Control (LAC).
The statement accused the Chinese of a "premeditated and planned action that was directly responsible for the resulting violence and casualties" and urged China to "take corrective steps".
Meanwhile, a Chinese statement quoted Mr Wang as saying: "China again expresses strong protest to India and demands the Indian side launches a thorough investigation... and stop all provocative actions to ensure the same things do not happen again."
Why were there no guns?
The Galwan river valley in Ladakh, with its harsh climate and high-altitude terrain, is close to Aksai Chin, a disputed area claimed by India but controlled by China.
This is not the first time the two nuclear-armed neighbours have fought without conventional firearms on the border. India and China have a history of face-offs and overlapping territorial claims along the more than 3,440km (2,100 mile), poorly drawn LAC separating the two sides.
The last firing on the border happened in 1975 when four Indian soldiers were killed in a remote pass in the north-eastern state of Arunachal Pradesh. The clash was variously described by former diplomats as an ambush and an accident. But no bullets have been fired since.
At the root of this is a 1996 bilateral agreement that says "neither side shall open fire... conduct blast operations or hunt with guns or explosives within two kilometres of the Line of Actual Control".
But there have been other tense confrontations along the border in recent weeks. In May Indian and Chinese soldiers exchanged physical blows on the border at Pangong Lake, also in Ladakh, and in the north-eastern Indian state of Sikkim hundreds of miles to the east.
India has accused China of sending thousands of troops into Ladakh's Galwan Valley and says China occupies 38,000 sq km (14,700 sq miles) of its territory. Several rounds of talks in the last three decades have failed to resolve the boundary disputes.