Theresa May said she hoped the European Union would respond "positively" to her approach to Brexit as senior Brussels figures warned trade talks may not be given the green light in December.
The British Prime Minister repeated her promise that the UK will "honour our commitments" amid speculation she is prepared to increase the amount she is prepared to pay in the divorce settlement with the EU.
Before talks with Taoiseach Leo Varadkar European Council president Donald Tusk and, Mrs May said she was looking forward to next month's Brussels meeting which could decide on whether to launch the next phase of Brexit talks.
The meetings will come in the margins of a summit in Gothenburg.
Arriving at the summit, Mrs May said: "We look forward to the December European Council. We are continuing to look through the issues.
"I was clear in my speech in Florence that we will honour our commitments.
"But of course we want to move forward together, talking about the trade issues and trade partnership for the future.
"I have set out a vision for that economic partnership, I look forward to the European Union responding positively to that so we can move forward together and ensure that we can get the best possible arrangements for the future that will be good for people in the United Kingdom and across the remaining EU27."
EU sources suggested Mr Tusk will tell Mrs May that although internal preparations had begun on preparing for the second phase of the Brexit process, covering a transitional deal and the future relationship the UK will have with Brussels, it could not be taken for granted that leaders will agree to move on to formal talks.
A Brussels source said: "Mr Tusk will inform Mrs May that such a positive scenario is not a given, it will require more work and that time is short.
"And he will ask Mrs May how the UK plans to progress on the three key issues for phase one."
The three issues where "sufficient progress" must be made include the financial settlement, citizens' rights and the border between Northern Ireland and Ireland.
The Taoiseach is likely to emphasise that progress is possible in December but "only if all sides show sufficient political will".
Mr Varadkar will use his meeting to emphasise the importance of upholding all aspects of the Good Friday Agreement, including the powersharing institutions, and will continue to urge the Northern Ireland parties to reach agreement.
Mrs May held talks with her Swedish counterpart Stefan Lofven on Thursday night.
He said the UK needs to clarify what the financial settlement would cover, and it was "very difficult to say" whether trade talks would be given the go-ahead in December.
If leaders do not agree to move to the second phase at the summit in Brussels on December 14-15, then it could mean no progress until the next scheduled European Council in March.
That would add to business uncertainty and increase the potential for the UK to leave without a Brexit deal.
The Gothenburg social summit brings together political leaders and other key players to discuss a new European Pillar of Social Rights for workers' rights.
Mrs May will take part in a working session on fair employment and working conditions and is expected to highlight the findings of the Taylor report published in July which examined the treatment of workers in the so-called gig economy.
She said: "In the UK we are rightly proud of the record rates of employment we have but as our economy grows I want to make sure we see a country and an economy that's working for everyone.
"I was very pleased when I first became Prime Minister to ask Matthew Taylor to look and do a review on modern employment practices.
"We will be talking about this today and it is an issue to which the Government will be responding later in the year.
"What we know is, as the world of work changes, it brings challenges as well as opportunities."
TUC general secretary Frances O'Grady said Mrs May "must reassure working people that a level playing field for workers' rights will be written into the Brexit deal".
"Britain's workers must not be left to fall behind the rest of Europe when future improvements are made," she added.
Brexit Secretary David Davis said that many EU nations were now keen to move on to trade talks, but notably omitted Germany and France from his list.
Speaking to the BBC in Berlin on Friday morning, Mr Davis said: "Many of them do want to move on. They see it as very important to them.
"Countries like Denmark, countries like Holland, countries like Italy and Spain, countries like Poland can see the big, big benefits in the future deal we are talking about.
"They have all got things to benefit from that. This is not a one-way street, this is not something for nothing, this is something that
Mr Varadkar suggested that the UK was unprepared for the difficulties its approach to Brexit would cause.
"I think it's certainly possible that we can come to conclusions in December allowing phase two talks to begin, but if we have to wait until the New Year, if we have to wait for further concessions, so be it," he said.
"But I think it would be in all of our interests that we proceed to phase two if we can in December.
"It's 18 months since the referendum, it's 10 years since people who wanted a referendum started agitating for one.
"Sometimes it doesn't seem like they have thought all this through."
He told reporters: "Britain having unilaterally taken the customs union and single market off the table, before we move to phase two talks on trade we want taken off the table any suggestion that there will be a physical border, a hard border, new barriers to trade on the island of Ireland."