In an address in the US last week, Mrs Braverman argued that multiculturalism had “failed” and called for international treaties such as the UN Refugee Convention and the European Convention on Human Rights (ECHR) should be reformed.
But former home secretary Dame Priti said her successor may have been trying to “get attention”.
Speaking on Sunday Morning With Trevor Phillips on Sky News, she said: “I don’t know what the intention was around that.
“It might just be to get attention, to have the dividing lines that previous commentators were mentioning as we go into the run-up to a general election.”
Dame Priti, who led the Home Office for three years under Boris Johnson, warned interventions such as speeches are “no substitute for action”.
The senior Conservative MP insisted the public wants to see results on the pledge to stop small boats crossing the Channel.
She said: “This side of a general election, if I might politely suggest it is about delivery and the Government will be judged on delivery.
“When you make pledges, statements and promises, you have to deliver.
“But of course pledges are no substitute for action. I think the public, they are sick of hearing about some of these issues and the failure to deliver.
“I think it is right that everyone puts a shoulder to the wheel and cracks on and does the work.”
The ally of Mr Johnson also took issue with Mrs Braverman’s comments about communities living separately.
She told host Sir Trevor: “You and I are sitting here today, we are the products of actual integration, multiculturalism, dynamic communities, people who love our country, want to contribute to our country, along with a hell of a lot of other people that have done exactly the same.
“I think that is something we should be proud of in our country.”
Ahead of the start of the Conservative Party conference in Manchester today, Mrs Braverman used a newspaper interview to criticise celebrities who spoke out against her speech.
She told the Mail On Sunday that celebrity critics are “out-of-touch pampered elites” who are “lecturing” the British public.