Speaking during a parliamentary debate, Philip Hollobone said individual fireworks are extremely dangerous.
But business minister Jo Johnson dismissed a ban and insisted current laws work well.
The debate came after a petition to restrict the use of fireworks attracted more than 100,000 names.
The petition, which called for restrictions on when fireworks can be used, was started by Jill Cutsforth, from Beverley, East Yorkshire, and Julie Doorne, from Sleaford, Lincolnshire in a bid to reduce stress and fear in people and animals.
But, Mr Hollobone, MP for Kettering, called for the government to go further.
He said: "I think there's great merit in saying all fireworks displays need to be licensed with a licensed operator, and frankly, amateur family-organised fireworks displays in people's back gardens are basically rubbish."
Labour's Angela Smith, a member of the the Environment, Food and Rural Affairs Committee, also backed the petition, arguing that restricting the number of days the public and organised events can set off fireworks should be restricted.
She said: "Ideally, we would end the use of fireworks in back gardens. But I do understand the difficulty in delivering that as policy."
Instead, she called for tighter regulations to govern how people use fireworks.
Mr Johnson acknowledged the concerns raised but said restricting their use to traditional holidays would be ineffective.
"It is likely that those who already use fireworks in an anti-social or inconsiderate way would not be deterred by further regulation," he said.
He added: "Restrictions in use could lead to a drop in legitimate sales, leading to job losses not only in the firework industry but independent and associated businesses."
Bracknell MP Phillip Lee also warned the debate that restricting the number of days that displays are permitted could reduce the viability of well-performing fireworks businesses.
The government said following the debate it would continue to monitor the situation closely.

Joseph Brown-Lartey died as his vehicle was split in half by a car driven by Addil Haroon in Rochdale in 2014.
Haroon, then 18, drove through a red light in a residential area at 80mph and was later jailed for six years.
Mr Brown-Lartey's father said it was like being "kicked in the teeth twice".
Mr Brown-Lartey was 25 when he died, and his father Ian said it was "very upsetting" that Haroon would be younger than that when he got out of prison.
"It's just like we've been kicked in the teeth twice. You lose your son and then the legal system that you trusted lets you down too," he said.
Dawn Brown-Lartey, Joseph's mother, said there was "no deterrent" to stop people driving dangerously.
"Judges are bound by guidelines and the guidelines need to be changed," she said.
Hours before the fatal crash, Haroon took a photo on his phone as his speedometer reached 142mph.
He messaged a friend with the words: "Leeds to Rochdale in 11 mins catch me."
In court, he admitted causing death by dangerous driving, causing death whilst unlicensed, causing death whilst uninsured and dangerous driving.
Brake's Roads to Justice campaign argues that families are "betrayed time and again by our justice system", and calls for tougher penalties for drivers who maim or kill.
According to a poll commissioned by the charity, 66% of people believe drivers who kill should be jailed for a minimum of 10 years.
The survey of 1,000 people also found 91% believe drivers who cause a fatal crash after drinking alcohol or taking drugs should be charged with manslaughter, which carries a possible life sentence.
Gary Rae, director of campaigns for Brake, said: "Drivers who kill while taking illegal risks are too often labelled 'careless' in the eyes of the law, and then given insultingly low sentences when their actions can only be described as dangerous and destructive."
Amateur home firework displays should be banned, in favour of licensed organised displays, a Tory MP has suggested.
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The parents of a man killed when his car was hit at high speed have put the wreckage on display at Westminster as part of a campaign for tougher sentences by road safety charity Brake.