The strategy includes measures to prevent young Muslims from being "radicalised", such as forging closer ties with those communities, and giving more support to mainstream Muslim voices in Britain.
Smith said 60,000 British workers, including shopping centre and hotel staff, would be trained to identify security threats, and help deal with future incidents.
"We need to tackle the causes of terrorism. We need to get in early to prevent people actually supporting violent extremism or supporting terrorism," she told BBC radio.
Many Muslims argue that the government's approach often portrays their whole community as the enemy.
The security strategy updates a 2003 policy based on the principles of prevent, pursue, protect and prepare.
The document says Britain possibly has the most numerous and capable al-Qaeda cells in Europe, and suggests deadlier weapons could be used.
"Changing technology and the theft and smuggling of chemical, biological, radiological and nuclear and explosive materials make this aspiration more realistic than it may have been in the recent past," the document said.
Britain has been a target for attacks since it joined the US in invading Afghanistan and Iraq after the September 11, 2001, attacks on the US.
In July 2005, suicide bombings on public transport in London killed 52 people.
More than 200 people have been convicted on "terrorism" related charges between 2001 and 2008.