Recent talks between ministers and Labor to end Brexit's impasse were "positive" and "productive," said the de facto MEP of the Prime Minister.
Later, David Lidington said he was "encouraged" by both sides that the talks should be "more urgent".
He said there will be more meetings between the parties this week.
Sue Hayman, Shadow Secretary of Labor, said there had been "genuinely constructive discussions" on Monday.
She said the two parties had "gotten a lot more into the details" and that they thought the government was "open to move in our direction."
Cross-party Negotiations have been taking place for several weeks after Theresa May's Brexit deal with the EU was effectively rejected by MEPs for the third time.
Ministers insist that they still seek MEPs' approval The terms of Britain's exit from the EU before 22 May, so that the country does not have to take part in the elections to the European Parliament a day later
For this purpose, number 1
The Mo Parliament talks were led by Federal Chancellor Philip Hammond, Brexit Secretary Stephen Barclay and Environment Minister Michael Gove.
The Labor team included Shadow Brexit Secretary Sir Keir Starmer, Shadow Chancellor John McDonnell and Ms Hayman.
Labor had previously complained that the government appeared unwilling to act in some key areas, in particular as regards the possibility of a customs union with the EU after Brexit.
BBC political correspondent Iain Watson said he understands this as an attempt to reach a compromise on this crucial issue in the coming days.
The Minister of the Cabinet, Mr. Lidington, said it was "not useful" to set a "tough and fast" deadline for talks and warned of a "cliff in itself that raises expectations".
But the tone of the comments after the meeting was generally more positive than on previous occasions.
- What are the Brexit points?
Ms. Hayman confirms that a "public vote" on Brexit was on the agenda For all her meetings and Labor, Labor explored "ways we can work with the government here."
Bur. Mr Lidington said it was not a government policy and the proposal had been voted in the House.
Former Shadow Law Attorney General Shami Chakrabarti said the Labor Front Benchers involved in the negotiations should tell Tuesday's National Executive Committee on Tuesday "whether there is any hope for a reasonable Brexit" or whether the only means to overcome the deadlock seems to be a second referendum or a general election.
On 31 October, the EU set a new deadline for Britain to leave.