The most signed e-petition on the No 10 website is one calling for convicted rioters to lose benefit payments.
"No taxpayer should have to contribute to those who have destroyed property, stolen from their community and shown a disregard for the country that provides for them," the petition argues.
It had more than 90,000 signatures at 6am and will be referred to the backbench business committee of MPs if it gets 100,000 signatures.
The MPs may then call a debate on it.
It comes as councils in Manchester, Nottingham and London say they will seek to evict social housing tenants who are convicted of violence locally and Housing Minister Grant Shapps says their powers could be extended to allow them to punish those who travelled out of the area to take part.
The e-petition, submitted by Stephen Mains, is dwarfing its closest competitors on the e-petitions website.
Its nearest rival, a bid launched by Conservative MP Robert Halfon to cut the price of petrol, had 24,000 signatures.
The next most signed e-petition was the campaign to retain the ban on capital punishment, which began in response to a less popular campaign to bring it back, signed by 20,000.
The most popular of the petitions calling for the return of the death penalty has been signed by 11,000 people.
There have been "technical problems" on the site since the petition about rioters went live - a government spokesman said it could be due to the volume of people trying to get onto the site but some people had still been able to get through.
Asked about the e-petition, a spokesperson for the Department of Work and Pensions said that, under current arrangements, "any benefit recipient who is convicted of an offence and is imprisoned, will lose their benefit entitlement".
Deputy PM Nick Clegg has also expressed sympathy with suggestions social tenants found to have been engaged in criminal activities should be evicted.
He told BBC London: "I think it's actually right to say if you go out and break the law and you destroy the community in which you live, why should you simply assume that you are going to continue to be supported in living in the way that you are in that community?"
Ministers have warned MPs not to "ignore" the public's suggestions.
Any petition signed by more than 100,000 UK citizens goes to the cross-party Commons backbench business committee, which will decide whether it is worthy of debate.
This does not mean any parliamentary bills will be tabled as a result, simply that the matter will be discussed.
Leader of the House of Commons, Sir George Young, told BBC News last week that the threshold for debating an e-petition could be raised if too many reached the signatures target.
He said: "We do want to monitor it to see if we've got the threshold either too high or too low.
"This is a new initiative and we've set 100,000 because we think that's roughly the right target, but if lots and lots of petitions sail through that barrier then we may need to see if it should be higher.
"If none of them are able to reach that target then we may need to lower it."
Labour have said the petitions could lead to debates on "crazy ideas".
The system replaces the previous e-petitions pages on the Downing Street website, set up when Tony Blair was PM.
The most popular of these, with more than 1.8 million people in support, opposed road pricing.
More than 70,000 backed the one-word suggestion that Gordon Brown should "resign".
And almost 50,000 signed up to the idea that TV presenter Jeremy Clarkson should become prime minister.
