Ch Con Brian Moore, who leads on anti-domestic violence measures for the Association of Chief Police Officers, told the BBC he believed people would welcome the initiative.
He said: "Many people listening to us will think, yes, if I knew that somebody was coming into my household as my new partner who was dangerous and who had been a previous abuser of people like me and my children, I would want to know."
However, Ms Smith was shouted down at a round-table discussion to mark the launch of of the consultation by a campaigner who accused her of "gimmicks" and "spin".
Sandra Horley, chief executive of Refuge, told the minister: "Police can't be expected to monitor relationships and love lives of offenders."
"The government is hoping to get away with useless initiatives like this register and it is hypocritical to sound tough and do little."
The announcement comes as the BBC learns an independent inquiry will be launched into the police handling of the fatal stabbing of a 24-year-old woman by her ex-partner.
Katie Summers, also known as Katie Boardman, was killed in a frenzied attack by Brian Taylor in October 2008.
Officers were called to Ms Summers' house in Farnworth, near Bolton, four times in the days leading up to her murder, it emerged.
The Independent Police Complaints Commission will examine whether police acted appropriately and what records they kept about the abuse.
Taylor was later convicted of Ms Summers' murder and sentenced to life in prison.
The latest Home Office figures for 2007/8 show 2.2% of women of any age said their partner used minor or severe force against them over the last year. The figure for men was slightly lower at 2.0%.
Across all age ranges, one in four women have been abused compared with one in six men.
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