Time is running out for a Brexit deal, leaders of European countries have warned ahead of more talks in Salzburg.
There is still no agreement on issues including how to avoid new checks on the Northern Irish border.
At the EU summit on Wednesday evening Mrs May stressed her "serious" proposals for future co-operation would ensure a "shared closed relationship".
European Commission chief Jean-Claude Juncker described her 10-minute presentation as "interesting".
"It was polite, it was not aggressive, she was doing her job," he told reporters as he arrived for a second day of talks.
Speaking to BBC Radio 4's Today programme, two of the EU leaders said they hoped the UK would hold another referendum on Brexit, in the hope of reversing the 2016 result.
Maltese Prime Minister Joseph Muscat said most of his counterparts would like the "almost impossible" to happen.
Andrej Babis, the Czech Republic's prime minister, added he hoped the British people might change their minds.
But Mrs May said there was no question of the UK seeking to extend its EU membership.
The UK is due to leave the EU on 29 March 2019, and both sides are trying to reach a deal in time, with a crunch summit specially convened in mid-November.