The 74-year-old Hazare, who has shed five kgs (11 lbs), spent the seventh day of his fast lying down on a makeshift stage at Ramlila grounds in New Delhi as electric fans cooled him in the humid monsoon heat. Temperatures reached into the mid-30s Celsius (95 Fahrenheit).
Hazare's supporters and the government said at the weekend they are open to talks, with Singh saying there was a "lot of scope for give and take."
But a prominent Hazare supporter said that the government had so far shown caution.
"The government sent an innocuous three page, unsigned note yesterday which summarised their position -- as if we need to know that," Kiran Bedi, a former police officer and one of India's best known anti-graft campaigners who works with Hazare, told Reuters.
Moves to open talks come as the Bharatiya Janata Party is organising a nationwide protest against the government on Thursday, while a group of left parties is planning a national protest on Tuesday.
Singh continued to strike a more conciliatory tone on Monday than when Hazare's fast first began after he was jailed by the government last week in a ham-handed move to thwart the hunger strike.
"The standing committee has the power to propose any amendment or amendments," Singh said in Kolkata, referring to a parliamentary body looking at an anti-corruption bill before parliament that lies at the heart of the standoff.
In another sign of possible compromise, Jairam Ramesh, a minister and Congress Party stalwart, publicly lent support to Hazare's demand that his team only negotiate with mediators from the prime minister's office or with Rahul Gandhi, the son of the Congress party chief, as opposed to a third party.
"That is a way out," Jairam Ramesh told reporters. He also said the government was mulling introducing a separate bill to tackle graft in the lower orders of bureaucracy, which had been another demand from Hazare.
With key state elections next year that pave the way for a 2014 general election, the government is keen to end a crisis that has paralysed policy making and parliament and added to Singh's unpopularity amid high inflation and corruption scams.
At least 50,000 people protested on Sunday to support Hazare and on Monday, a holiday in the capital, thousands came again carrying flags, banners and shouting slogans like "long live the revolution."
Hazare's campaign has struck a chord with India's rising middle class, many sick of endemic bribes and angry at a series of corruption scandals that have touched top politicians and businessmen in Asia's third largest economy.
Hazare's team members have said this is not a fast to death -- he is also drinking water. The activist has carried out scores of hunger strikes against governments in the last few decades.
"Our demand that they pass the bill by the end of the month remains unchanged. It's what the people want," Bedi said.
Criticism of Hazare's hunger strike has also surfaced from activists who say it is setting a bad precedent by holding democratic institutions hostage.
"While his means may be Gandhian, Anna Hazare's demands are certainly not," Booker prize-winning novelist and social activist Arundhati Roy wrote in The Hindu newspaper.
"The (Hazare) bill is a draconian anti corruption law in which a panel of carefully chosen people will administer a giant bureaucracy."
In another sign of the tentative efforts by a fumbling government to take the initiative, a Congress party lawmaker has also sent Hazare's bill to a parliamentary committee for consideration, meeting a demand of the protesters.
"The government and Team Anna are in back channel negotiations. So that's a start," said Anirudh Goenka, a 36-year-old social worker, at the protest. "Maybe we will not achieve everything the Jan Lokpal set out to do, but even a compromise is a way forward."
Hazare was briefly jailed last Tuesday, a move the government sought to reverse quietly. But he refused to leave prison until the government allowed him to continue his vigil, in public, for 15 days. He was released on Friday to huge cheering crowds and widespread media coverage.
For many, the pro-Hazare movement has highlighted the vibrant democracy of an urban generation that wants good governance rather than government through regional strongmen or caste ties -- a transformation that may be played out in 2012 state polls.
Several scandals, including a telecoms bribery scam that may have cost the government up to $39 billion, led to Hazare demanding anti-corruption measures. But the government bill creating an anti-graft ombudsman was criticised as too weak as it exempted the prime minister and the judiciary from probes.
