Boris Johnson has promised a renewed effort to secure a deal with the EU before the Brexit deadline.
The UK’s Brexit negotiators will now meet their EU counterparts twice a week next month, in the run up to a crucial summit on October 17-18.
It follows a backlash from MPs and opponents of a no-deal Brexit against the prime minister’s decision to suspend Parliament next month.
The EU said it expected the UK to come up with “concrete proposals”.
A European Commission spokesperson said its “doors remain open” and insisted it had “demonstrated our willingness to work 24/7 throughout this long process”.
Mr Johnson said he had been “encouraged” by the response from EU leaders but said “it is now time for both sides to step up the tempo”.
He also said he had seen “a willingness to talk about alternatives to the anti-democratic backstop”.
The backstop, which aims to prevent a hard border on the island of Ireland after Brexit, is likely to be at the forefront of the twice weekly discussions between Brussels and the UK prime minister’s lead negotiator, David Frost.
The government reiterated that a new deal would not be agreed unless the withdrawal agreement is reopened and the backstop taken out.
No 10 said the two sides “remain some distance apart on key issues” but added they were “willing to work hard to find a way through”.
The UK is currently set to leave the EU on 31 October with or without a deal.
The withdrawal deal, agreed between Mr Johnson’s predecessor Theresa May and the EU, was repeatedly rejected by MPs.
Mr Johnson says while he would prefer a deal he is willing to leave without one – and maintains the UK will leave by the October deadline “no ifs no buts”.
On Wednesday, the prime minister asked the Queen to suspend Parliament for five weeks in September and October, saying he would outline his “very exciting agenda” in a Queen’s Speech on 14 October.
But several MPs argue the suspension is designed to stop them from blocking a no-deal Brexit, by denying them enough time to debate.
What are MPs’ plans to stop no deal?
The former Justice Secretary David Gauke – who resigned over Mr Johnson’s openness to a no-deal Brexit – told the BBC that next week could be MPs’ “only opportunity” to challenge no deal.
He said the public did not want a no-deal Brexit, but the options of those opposed to such an exit have “now narrowed”.
Labour leader Jeremy Corbyn vowed to “challenge” Mr Johnson on what he described as “a smash and grab raid against our democracy,” when Parliament returns from recess on Tuesday.
Mr Corbyn has also said tabling a no-confidence motion in the prime minister at an “appropriate moment” also remained an option.
Can the rebel alliance stop no-deal Brexit?
Within days we will know if the MPs who are implacably opposed to leaving the EU without a deal can really stop that happening.
With lots of former ministers on the backbenches, the group which is openly fighting against the possibility of leaving the EU without a deal has a different complexion.
And the opposition parties, including the Labour leadership, now appear fully engaged in next week’s plan.
But given Boris Johnson’s main reason for success in the Tory leadership election was to leave the EU whatever it takes at the end of October, it is a pretty major goal for a group of backbenchers and opposition politicians.
BBC Newsnight’s political editor Nick Watt said a cross-party group of MPs was planning a “surgical strike” to change the law and ban the UK from leaving the EU without a deal.
It would involve an emergency debate on Tuesday and a vote to take control of the Commons agenda the following day. That could prevent Chancellor Sajid Javid from carrying out his spending review, scheduled for Wednesday.
Our correspondent said one possibility was a one-line amendment to the Withdrawal Act, saying the UK can only leave the EU with a deal in place.
But he said the group face a tight deadline, with only two working days before Mr Johnson is expected to suspend Parliament.
The plan also faces challenges in the House of Lords, where Brexiteers could table multiple amendments as a delaying tactic until the shutdown begins, he said.
It is thought some MPs are exploring ways of ensuring Parliament can meet on the Friday, Saturday and Sunday before the planned suspension.
What have other parties said?
Opposition parties have released a joint statement condemning the “undemocratic actions” of the prime minister and calling for the suspension to be reversed immediately.
“The prime minister is shutting down Parliament with the sole aim of stopping MPs from avoiding a no-deal Brexit,” said a statement from Labour, the SNP, the Lib Dems, Plaid Cymru, the Independent Group for Change and the Green Party.
“This will be the longest prorogation in recent history, and one that comes at a critical moment in the history of our respective nations and the Brexit process.”
Leader of the DUP Arlene Foster, however, welcomed the decision but said the terms of her party’s agreement with the Conservatives would now be reviewed.
Mr Johnson has a working majority in Parliament of one and support from the DUP keeps the Conservative Party in power.
What other reaction has there been?
Some Tories have also objected to the five-week suspension. Government whip Lord Young has resigned in protest, arguing the move risks “undermining the fundamental role of Parliament”.
Commons leader Jacob Rees-Mogg said this parliamentary session had been one of the longest in almost 400 years, so it was right to suspend it and start a new session and outrage at the plan was “phoney”.
But Ruth Fox – director of parliamentary experts the Hansard Society – said this prorogation was “significantly longer than we would normally have” for the purpose of starting a new parliamentary session.
In Scotland a judge is considering a legal attempt brought by parliamentarians to block Parliament’s suspension. His decision is due at 10:00 BST on Friday.
The planned suspension also triggered protests across the country, with further demonstrations expected this weekend.
Meanwhile, an e-petition on the government’s website demanding Parliament not be suspended has reached more than 1.5m signatures.