Although the heavy rains have receded in recent days, efforts to reach those stranded—mainly pilgrims who were visiting Hindu shrines in remote areas—have been hampered by extreme damage to bridges and roads due to landslides, and by a lack of rescue equipment.
"The government has not yet been able to determine exact figures on the number of deaths, injuries, and missing persons due to lack of connectivity with the flood-affected areas," said Anil Chandola, a government official in Uttarakhand, the Himalayan state that has borne the brunt of the flooding.
People are "still trying to get in touch with families," he said.
On Friday morning, Indian television channels, citing unnamed officials, said around 14,000 people were still missing.
But Kuldeep Dhatwalia, a Home Ministry spokesman, said that figure was incorrect. The government, he said, believes around 50,000 people remain stranded, but they weren't considered missing.
Authorities have rescued some 33,000 people, officials said.
Monsoon rains that started June 15 triggered floods and landslides in Uttarakhand and the neighboring state of Himachal Pradesh.
At least 550 people died in Uttarakhand state alone, and at least 20 in Himachal Pradesh, officials said Friday. In neighboring Nepal, authorities said 39 people had died and 20 people were missing.
Television news has shown video in recent days of houses and bridges collapsing into torrents of water as the ground gave way under them. One pilgrimage town in Uttarakhand, Kedarnath, was devastated by a flash flood on June 15.
The Indian government has deployed more than 25,000 soldiers and 43 Air Force helicopters to assist with rescue efforts in Uttarakhand and Himachal Pradesh. Authorities are airdropping food packets and medicines to villages cut off by the rains.
Anand Sharma, director of Uttarakhand's state meteorological center, said water levels were receding due to the lack of rain over the past few days. But he said there was a chance of "slight rainfall at a few places" in the state in coming days.
Every year, people trek to four shrines—Kedarnath, Badrinath, Gangotri and Yamunotri—as part of the Char Dham pilgrimage. From May to October, Kedarnath Temple alone receives around 5,000 pilgrims a day, temple authorities say.
Uttarakhand's Agriculture Minister Harak Singh Rawat described the floods as the "worst tragedy of the millennium."
"It will take us at least five years to recover from the extensive damages caused to the entire infrastructure network in the Kedarnath area," he said.
Parts of New Delhi and its suburbs also have been hit. Thousands of people were evacuated from houses near the Yamuna River in Delhi this week and moved to tent villages. By Friday, the river's level was receding, officials said.
The southwest monsoon this year has advanced over India at the fastest rate in more than half a century, covering the country by last weekend, about a month ahead of normal. The last time the annual rains spanned the entire country at such speed was in 1961.
—Krishna Pokharel contributed to this article.