There were no major breakthroughs at the meeting between UK Prime Minister Boris Johnson and his Irish counterpart Taoiseach Leo Varadkar over the Irish border backstop.
Both leaders said in a joint statement that the Monday meeting in Dublin was "positive and constructive".
The statement said "common ground was established" but that important gaps remain. However, no details were provided.
The heads of state will try to meet again in the near future.
Johnson's government confirmed it would suspend parliament on Monday until October 14, limiting MPs' ability to block Johnson's plans for Brexit.
MPs who are trying to stop a no-deal Brexit called the suspension a "coup".
Earlier in a press briefing with Varadkar, Johnson said: "I have one message that I want to land with you today, Leo, that is I want to find a deal. I want to get a deal."
"Like you, I've looked carefully at no-deal, I've assessed its consequences both for our country and yours.
"And yes, of course, we could do it, the UK could certainly get through it but be in no doubt that this outcome would be a failure of statecraft for which we would all be responsible.
"So for the sake of business, for farmers, and millions of ordinary people who are counting on us to use our imagination and creativity to get this done. I want you to know I would overwhelmingly prefer to find an agreement."
Varadkar said that the backstop was a "critical component" of the Withdrawal Agreement unless "alternatives were found" but that the EU had not received any alternative proposals yet.
He added that he was "confident" that he would be able to "find some common ground" with Johnson during their meeting.
The British PM reiterated that the UK must come out of the EU by October 31.
"I know that Brexit was not a conundrum that Ireland wished for and there are questions that we need to resolve," added Johnson.
The UK prime minister said there were three questions that must be answered: "Can we ensure that we have unchecked movement at the border? I think we can," said Johnson. "The UK will never institute checks at the border and I hope our friends in the EU would say the same."
The second question for Johnson was if "we can uphold the Good Friday agreement" and the answer was yes for him.
And finally: "Can we protect the economic unity of the gains of Ireland? Yes," he said.
"I think we can achieve these things while allowing the UK to exit the EU," Johnson added.
Varadkar said he would be keen to have the matter resolved with a Brexit deal at the next EU summit on October 17.
He added that a request for an extension is not what most EU members want but that "there was good reason to consider it".
Johnson said he had proposals to change the Withdrawal Agreement but that he wouldn't share them with the public.
Varadkar said that the absence of a backstop in a proposal would be the same as no-deal for Ireland.
When asked about the UK Parliament's bid to block a general election as well as a no-deal, Johnson answered he was "undaunted" by the dissent he was facing in the Commons.
You can watch the full press conference back in the above video player.