Her comments prompted strong criticism from campaigners, while the United Nations’ refugee agency (UNHCR) rejected her call for the definition of who qualifies for protection to be “tightened”.
Using her address at the American Enterprise Institute, a centre-right think tank in Washington DC, Ms Braverman set out a blueprint for international efforts to tackle the refugee crisis.
The senior cabinet minister has previously taken aim at the European Convention on Human Rights (ECHR), signed in 1950, claiming it restricted the government’s efforts to introduce tough policies such as the scheme to send some migrants arriving in Britain to Rwanda.
Ms Braverman described the UN convention as “an incredible achievement of its age”.
“But more than 70 years on, we now live in a completely different time,” she added, telling the audience: “According to analysis by Nick Timothy and Karl Williams for the Centre for Policy Studies, it now confers the notional right to move to another country upon at least 780 million people.
“It is therefore incumbent upon politicians and thought leaders to ask whether the Refugee Convention, and the way it has come to be interpreted through our courts, is fit for our modern age, or whether it is in need of reform.”
She also argued that tests for how refugees are defined have changed, lowering the threshold for claiming asylum.
“Let me be clear, there are vast swathes of the world where it is extremely difficult to be gay, or to be a woman," Ms Braverman said.
"Where individuals are being persecuted, it is right that we offer sanctuary.
“But we will not be able to sustain an asylum system if in effect simply being gay, or a woman, and fearful of discrimination in your country of origin is sufficient to qualify for protection.
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“The status quo, where people are able to travel through multiple safe countries, and even reside in safe countries for years, while they pick their preferred destination to claim asylum, is absurd and unsustainable," she added.
The UNHCR, which released a statement shortly after her speech, said there was no need for reform “or more restrictive interpretation, but for stronger and more consistent application of the convention and its underlying principle of responsibility-sharing”.
The agency said the Refugee Convention “remains as relevant today as when it was adopted”, and added: “Where individuals are at risk of persecution on the basis of their sexual orientation or gender identity, it is crucial that they are able to seek safety and protection.”
As Ms Braverman mulled over reform of the convention ahead of her US visit, her ideas were welcomed by the chairman of campaign group Migration Watch UK.
Alp Mehmet said she was right to “call out the conventions” and suggested Britain should withdraw from both the ECHR and the Refugee Convention if reforms were not made.
But the Refugee Council warned the UK should be “addressing the real issues in the asylum system, such as the record backlog, and providing safe routes for those in need of protection”, rather than tearing up agreements.
Nearly 24,000 people have been detected crossing the English Channel in small boats this year so far, despite Rishi Sunak’s promise to “stop the boats”, though the number of crossings are down from last year.
The government’s plans to deal with high levels of unauthorised migration have stalled, with the Rwanda plan tied up in the courts, while attempts to accommodate 500 migrants on a barge off the Dorset coast are on pause after the deadly bacteria Legionella was detected aboard.