Council estate resident groups in England will be able to apply for anti-social behaviour orders, under measures announced by the government.
Ruth Kelly said improvements were needed inside and outside homes
The tenant management organisations will be assessed before being allowed such powers, with "clear safeguards" to make sure they are not abused.
Asbos ban people from continuing specific anti-social behaviour or from being in certain areas.
Tony Blair said the powers would allow people to take "swift action".
Asbos are a key plank of the government's "respect" agenda, but separate reports from the Home Office and the National Audit Office in December found that between 47% and 55% have been breached in England and Wales.
Communities Secretary Ruth Kelly, appearing with the prime minister as the row continued over her decision to send her son to a private school, also announced £485 million would go to update about 55,000 run-down council housing this year.
She said the powers and funds were a step towards "making sure that the improvements we want to see are happening both inside and outside the home".
The increased powers add to areas of responsibility that the management groups already have, such as rent collection, house allocations and lettings.
"No-one knows better how to transform a community than the people that live there," Mr Blair said.
"Local people are increasingly playing a bigger role in the decisions that affect them and the areas in which they live."
The modernisation budget since 2002 rises to £3.7bn with the latest addition.
It will be used by 17 local authorities to bring their housing up to standard under the government's Decent Homes programme.
The government said a million council homes had been improved since 1997, with 500,000 new kitchens, 350,000 new bathrooms and 630,000 new boilers installed.
"Poor housing can make areas unpopular to live in and create a bad reputation," Ms Kelly said.
"The ongoing investment we are putting into decent homes together with the growing role for tenants in shaping their own environments is transforming not just individual homes but entire communities."
The National Federation of ALMOs (arms-length management organisations which have the same role as tenant management organisations) said it was a "major landmark" in allowing tenants to make decisions regarding their communities.
"This announcement is indicative of the increasing importance the government is placing on tenant-led social housing models such as ALMOs, and how a broader, community focus is needed to improve the country's social housing estates," said federation chairman Dennis Rees.