More than nine out of 10 parents said they would support random searches to detect pupils committing these offences, an exclusive TES poll reveals.
Parents also supported a "zero tolerance" policy of automatic expulsion for those caught with weapons or drugs.
Eight out of 10 said they favoured permanent exclusion for pupils who deal in cannabis, while more than seven out of 10 favour the same sanction for children caught with knives.
The findings follow a call by the Prime Minister this year for headteachers to carry out random searches and drug tests.
He was quick to point to parents' positive perception of improvements in behaviour as evidence that policies to tackle indiscipline are working.
Mr Blair said: "I am pleased to see that our drive to improve behaviour in schools is delivering results, and welcome parents' support for the tough measures we have taken as well as the power to drug test pupils and exclude and prosecute them for possessing weapons."
The poll of 1,000 parents in England and Wales, carried out by FDS International, also shows strong support for a hard line against pupils who assault teachers - although three out of 10 said they did not think it warranted permanent exclusion.
Parents take a more tolerant view of pupils who threaten teachers but stop short of assault. Less than a quarter believe such threats should result in expulsion - nearly half (47 per cent) favour temporary exclusion, while more than a quarter (28 per cent) believed a letter home would be sufficient and 9 per cent favour letting pupils off with a detention.
The survey also showed that parents make a clear distinction between pupils caught in possession of cannabis and those who sell it to others. Less than half of parents believe possession should lead to permanent exclusion.
Overall, parents have positive views about standards of behaviour in their own children's schools - 35 per cent believe it has improved over the past five years, against 30 per cent who think it has deteriorated.
But parents of secondary school pupils still believe the biggest problem facing schools is disruptive or badly behaved pupils.
Those with children at primary school believe behaviour is less of an issue, rating it the third-biggest problem behind underfunding and lack of resources and overcrowded classes.
This parental optimism comes in spite of a series of high-profile incidents of violence, including the fatal stabbing last year of 14-year-old Luke Walmsley at Birkbeck school in Lincolnshire.
The National Association of Schoolmasters Union of Women Teachers has been pressing for the introduction of airport-style metal detectors in schools to find guns and other weapons.
The working group on school security, which was set up after headteacher Philip Lawrence was fatally stabbed in 1995, is now reviewing what can be done to keep weapons out of schools including the use of X-ray machines and metal detectors.