Members of industry groups welcomed the partial resumption of activity but said a large number of businesses faced bottlenecks due to a lack of raw materials and police restrictions on the movement of workers.
India has reported 24,942 cases of COVID-19, the disease caused by the coronavirus, and 779 deaths. The authorities have set up teams to focus on compliance with lockdown measures.
In a letter to Prime Minister Narendra Modi, the president of the main opposition Congress party, Sonia Gandhi, said small businesses faced economic ruin and job losses due to the absence of any major support from the government.
She called for a fiscal package of at least one trillion rupees ($13 billion) to protect wages of employees in small businesses and to provide credit guarantees on bank loans.
"Every single day of the lockdown comes at a cost of 30,000 crore ($3.9 billion) to the sector," she said.
In Modi's home state of Gujarat, authorities allowed software and IT companies to start operations on Saturday with up to 50% of their staff though some industry bodies urged members to start with only 10% to 15% of the workforce.
"It is crucial to avoid a rush of employees to offices to prevent spread of coronavirus," said Maulik Bhansali, chairman of Gujarat Electronics and Software Industries Association.
Authorities in the eastern state of Odhisha allowed stranded labourers to travel within the state for work.
In Pakistan, the government extended a nationwide lockdown until May 9. However, it is switching to a "smart lockdown" from Saturday with targeted tracking and tracing of cases while allowing some industrial and commercial activities to resume under safety guidelines.
"Isolating these cases and their contacts will improve our ability to contain the disease alongside allowing the economy to function and people to get employment," said planning minister Asad Umar, who oversees Pakistan's coronavirus response body.
"This upcoming month of Ramadan will be decisive," he said, emphasising that adhering to the government's virus containment measures would allow other parts of the economy to restart.
Prayer congregations for Ramadan have also been allowed in Pakistan with the exception of the southern province of Sindh, where doctors have warned the virus could spread rapidly.
In Karachi, the capital of Sindh and Pakistan's largest city, most mosques were closed for Ramadan evening prayer gatherings, which began on Friday.
Bangladesh extended its nationwide lockdown to May 5 and ordered mosques to restrict attendance at Ramadan evening prayers to 12 people.
Sri Lanka extended the temporary suspension of SriLankan Airlines to May 15, and said requests from its migrant workers to return to the country would be considered only after the eradication of coronavirus cases in the country.
Sri Lanka has more than 1.2 million people working abroad, mainly in the Middle East, Italy and South Korea.
"Please do not put Sri Lankan government unnecessarily in a difficult situation and if you love your motherland, please stay safe in wherever you are." said Kamal Ratwatte, chairman of Sri Lanka Bureau of Foreign Employment in a statement.
Here are official government figures on the spread of the coronavirus in South Asia:
* India has reported 24,942 cases, including 779 deaths * Pakistan has reported 11,940 cases, including 253 deaths * Afghanistan has reported 1464 cases, including 47 deaths * Sri Lanka has reported 435 cases, including seven deaths * Bangladesh has reported 4,998 cases, including 140 deaths * Maldives has reported 34 cases and no deaths * Nepal has reported 49 cases and no deaths * Bhutan has reported seven cases and no deaths
($1 = 76.2600 Indian rupees)
(Additional repoting by Sumit Khanna in Ahmedabad, Jatindra Dash in Bhubneswar, Waruna Karunatilake in Colombo, Ruma Paul in Dhaka, Gopal Sharma in Kathmandu and Orooj Hakimi in Kabul; Writing by Rupam Jain; Editing by David Clarke) ((Rupam.Jain@thomsonreuters.com; +91 7042133028;))