However, Remain ministers are increasingly concerned that it means the Prime Minister will delay a vote on her deal until just days before Britain leaves the EU.
One said: "She has to bring her deal for a vote in the first half of March. If she leaves it until after the 20th, she will face resignations. She cannot just run down the clock."
Brokenshire said: "I think that gives that sense of timetable, clarity and purpose on what we are doing with the EU - taking that work forward and our determination to get a deal - but equally knowing that role that Parliament very firmly has."
In a bid to make a breakthrough, Stephen Barclay, the Brexit Secretary, is meeting Michel Barnier, the EU's chief negotiator, for the first time and Jeremy Hunt, the Foreign Secretary, will visit Paris and Warsaw for talks this week.
On Friday, MPs will consider a motion on Brexit and a series of amendments, likely to include an attempt by Labour's Sir Keir Starmer to force May to hold a vote on her deal on February 26.
Brokenshire acknowledged that more work was needed to get the UK ready for Brexit on March 29, telling the BBC that there are "still steps that are currently being put in place".
Starmer earlier said his plan was necessary to put a "hard stop" to May "running down the clock" before the March 29 deadline.
He told the Sunday Times he feared the Prime Minister was "pretending to make progress" but actually intended to return to Parliament after the March 21-22 European Council summit the week before Brexit and offer MPs a "binary choice" - her deal or no deal. "We can't allow that to happen," he said.
Two Labour MPs are also expected to table an amendment this week that would offer MPs the chance to support the Withdrawal Agreement but would specify that, if passed, Britain could only leave if it was put to the public for a second referendum.
It is thought that Tory MPs including Dominic Grieve and Anna Soubry are prepared to back the amendment.