He also told MPs the British and Irish governments "recognise the benefits" that come from the travel area.
Mr Brokenshire was responding to questions from East Belfast MP Gavin Robinson and Foyle MP Mark Durkan.
He said said he did not "want to see a return to the borders of the past".
It was Mr Brokenshire's first appearance at Northern Ireland Questions since he was appointed secretary of state last week.
He was also asked about the possibility of holding a border poll and repeated his view that the "conditions had not been met".
DUP deputy leader Nigel Dodds told the House that a united Ireland would be "financially catastrophic".
Mr Brokenshire appeared in the Commons alongside the new Northern Ireland Minister Kris Hopkins, who succeeded Ben Wallace.
Shadow Northern Ireland Minister Stephen Pound joked that he had now faced six Conservative ministers and he suggested he was being used "as a training aid for young thrusting Tories".
Shadow Northern Ireland Secretary Dave Anderson said the Conservative government was "badly prepared for Brexit" and he urged Mr Brokenshire to read recent reports which highlighted the economic difficulties.
The secretary of state said he was "always grateful for summer reading" and he said he would add the Labour MP's suggestions to his list.
Mr Brokenshire's predecessor Theresa Villiers was an interested observer during the session of Northern Ireland Questions, which is the last before the summer recess.

The crash happened on the A18 Mountain Road, in the vicinity of the Mountain Box, at about 07:50 GMT.
Police said the man was driving towards Ramsey in a white Citroen Berlingo when it was in collision with a blue Ford Transit coming the other way.
The Transit driver was taken to hospital but his injuries are not believed to be life-threatening.
Det Insp Mark Newey said the family of the driver who died have been informed.
The road was closed for several hours following the crash and witnesses are asked to contact police headquarters.

The force has urged bargain hunters to refuse to buy illicit food, alcohol, fashion, medicines and beauty goods, which could contain hidden dangers.
Make-up laced with paint stripper was another product highlighted at a summit being held in Edinburgh on counterfeit goods and criminal gangs.
The event includes speakers from Interpol and US Homeland Security.
Scottish Justice Secretary Kenny MacAskill said: "Buying counterfeit goods might be seen as a victimless way to get presents for family and friends on the cheap, but many of these items will have a long back story of criminality, often involving violence.
"However, the problem doesn't just lie with fake bags, perfume or alcohol.
"There is a serious global problem in counterfeit medicines, machinery and engine parts which can be seriously damaging to people's health and potentially deadly."
Mandy Haeburn-Little, director of summit organiser the Scottish Business Resilience Centre, said: "Everyone loves a bargain. But people need to stop to think about the true cost of fake goods. Can you be confident that those cheap cigarettes, perfumes and alcohol are actually safe?
"However, it goes much deeper as those products are likely to have supported child labour or human trafficking or used to fund serious organised crime.
"Illicit trade also hurts businesses in Scotland very hard. People choosing bargains at markets, car boot sales or on the internet impacts hugely on retailers and manufacturers - less genuine goods being sold closes businesses and puts people out of work."

The 25-year-old former Ipswich Town youngster has made more than 230 appearances for the U's, but was hampered by injury last season.
Contract options have also been taken up for defenders Lewis Kinsella, Kane Vincent-Young and winger Drey Wright.
Wright, 22, has featured 101 times for the U's, while Kinsella, also 22, joined from Aston Villa last summer.
Vincent-Young, 21, featured 23 times last season for the U's.
Secretary of State James Brokenshire has told the House of Commons the continuation of the Common Travel Area between Northern Ireland and the Republic will be a "priority issue".
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Dog skin boots and perfume containing urine were among a range of fake goods seized by Police Scotland.
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Colchester United defender Tom Eastman has signed a new two-year contract with the League Two side.