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.
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".