* May to put her case over dinner on Thursday
* Move on EU citizens' rights changes focus before summit
* EU leaders say not enough progress to warrant trade talks (Adds May, Corbyn comments)
BRUSSELS, Oct 19 (Reuters) - Prime Minister Theresa May urged the European Union on Thursday to break the deadlock and move forward with Brexit talks, asking the bloc's leaders to respond with "urgency" on easing the fears of their citizens living in Britain.
Arriving at a two-day summit in Brussels with other EU leaders, May sought to lower any remaining expectation that she could win a breakthrough in the talks to unravel more than 40 years of union. Instead, she turned the focus to making progress in the coming weeks, particularly on citizens' rights.
Weakened by losing her Conservative Party's majority in a June election and failing to rally support at an ill-fated party conference, May cannot move on the EU's insistence on increasing her pay offer for the divorce agreement.
She is hamstrung by demands in her own party for her to walk away unless the EU agrees to moving the talks forward to discuss trade, and Germany which does not want to be left with a large bill when Britain leaves the bloc in March 2019.
"We'll ... be looking at the concrete progress that has been made in our exit negotiations and setting out ambitious plans for the weeks ahead. I particularly, for example, want to see an urgency in reaching an agreement on citizens' rights," May told reporters.
But she avoided questions about increasing the amount Britain is willing to pay when it leaves the EU, instead referring back to a speech last month in Italy when she outlined an offer of around 20 billion euros ($24 billion) to try to improve the tone.
"That speech ... set out that ambitious vision and I look forward to us being able to progress that in the weeks ahead," she said.
Without a new offer on the money, May has attempted to change the focus by offering concessions on the protection of the rights of around 3 million EU citizens living in Britain, promising to make it as easy as possible for them to stay.
On her Facebook page, May wrote that "we are in touching distance of agreement" and asked the EU to show the "flexibility and creativity" to secure a deal in the coming weeks.
While welcome, this is unlikely to alter the outcome of the Brussels summit, where on Friday morning, when May has left, the bloc is expected to say the Brexit talks had not yet made enough progress for them to open the post-Brexit trade negotiations.
CHANGE OF TACK
That lack of movement has increased the pressure on May from her own party, particularly a small number of Brexit campaigners who have long said that the prime minister should walk away from the talks if the EU did not move them forward.
In an open letter to May on Thursday, pro-Brexit lawmakers and business people said that unless the talks moved to trade, Britain should signal it is ready to be subject to World Trade Organization (WTO) rules from March 30, 2019, when Brexit takes effect.
The government says it does not want to crash out of the EU and is working to secure a deal. But comments that ministers are planning for the possibility of a no deal have been pounced on by the Britain's main opposition Labour Party.
Jeremy Corbyn, whose party has matched and sometimes beats May's Conservatives in the opinion polls, arrived in Brussels on Thursday to meet EU lawmakers to try to break "the Brexit logjam" created by what he called government "bungling".
Seen as having little chance of becoming prime minister last year, Corbyn is now being listened to in Brussels and was due to meet the bloc's chief negotiator, Michel Barnier, and other officials on Thursday.
Recognising May's position at home, EU leaders are expected to make a "gesture" by telling EU staff to prepare for talks on a transition period needed to ease uncertainty for business. But they warn there is still a lot to be done.
"We have to work really hard between October and December to finalise this so-called first phase and to start negotiating on our future relationship with the UK," Donald Tusk, the chairman of EU leaders, said on Wednesday. ($1 = 0.8454 euros) (additional reporting by William James and Estelle Shirbon in London, Philip Blenkinsop and Gabriela Baczynska in Brussels; Editing by Alison Williams)