Russia has recorded its highest daily surge in coronavirus cases since July as India's total infections surpassed 5.7 million and Chinese authorities eased entry restrictions as COVID-19 rates in the country dwindled.
Health officials in Russia reported 6595 new coronavirus cases on Thursday, the highest daily rise since July.
In Moscow, more than 1000 new cases were recorded for the first time since June.
The number of daily new cases started to grow in late August in Russia, which has the fourth largest caseload in the world at 1.12 million infections.
There have been nearly 20,000 confirmed deaths.
Officials have repeatedly dismissed speculation of a second lockdown, saying the increase was expected and Russia's health care infrastructure was prepared for it.
India reported another 86,508 new cases on Thursday but Prime Minister Narendra Modi said he sees little merit in imposing even short local lockdowns.
India has confirmed more than 5.7 million cases, the second-most in the world.
The health ministry also said on Thursday that 1129 more people have died for a total of 91,149.
India's junior Railways Minister Suresh Angadi died on Wednesday, nearly two weeks after he was admitted to a New Delhi hospital with COVID-19.
He was the first federal minister and the fourth Indian politician to die from the disease.
Modi on Wednesday decried short, local lockdowns imposed in some places and said the country needs to not only keep fighting the virus but also move ahead boldly on the economic front.
He asked states to focus on testing, tracing, treatment and surveillance.
He said lockdown restrictions hit smooth movement of goods and services, including medical supplies.
Meanwhile, foreigners holding certain types of visas and residence permits will be permitted to return to China starting from next week as the threat of coronavirus continues to recede.
The new regulation lifts a months-long blanket suspension covering most foreigners apart from diplomats and those in special circumstances.
Beginning on Monday, foreign citizens holding valid Chinese visas and residence permits for work, personal matters and family reunions will be permitted to enter China without needing to apply for new visas, according to the regulation.
Those whose permits have expired can reapply.
Returnees must undergo two weeks of quarantine.
The announcement was made by the Ministry of Foreign Affairs and the National Immigration Administration on Wednesday.
Authorities announced seven new cases of coronavirus in China on Thursday, all of them from people who had come from overseas, marking 39 days since the country has reported a case of domestic transmission.
China has confirmed 85,314 cases of COVID-19 since the virus was detected in Wuhan late last year.
Israel has moved to further tighten its second countrywide lockdown as cases continue to soar.
The cabinet voted on Thursday to close all non-essential businesses including open-air markets.
It agreed that prayers and political demonstrations should be limited to open spaces and no more than 20 people and that participants would not be able to travel more than a kilometre from home to attend either.
The measures are set to go into force on Friday afternoon as the country shuts down for the weekly Sabbath.
The restrictions on demonstrations are subject to approval by the Knesset, Israel's parliament, and the limits on both prayers and protests could spark a backlash.
Israel is reporting nearly 7000 new cases daily, making the outbreak in the country of 9 million people among the worst in the world on a per capita basis.
Globally, more than 31.99 million people have been reported to be infected by the coronavirus and 977,327 have died.
Australian Associated Press