By Elizabeth Piper and Robin Emmott
BRUSSELS (Reuters) - Prime Minister Theresa May defended her offer to guarantee EU citizens living in Britain broadly the same rights as Britons on Friday, saying differences could be overcome by a "constructive" attitude to Brexit talks.
In the first test of her negotiating strength after losing a parliamentary majority at a June 8 election she did not need to call, May responded to criticism by other EU leaders at a summit of the offer, which one described as "inadequate".
The 60-year-old leader, who was once in control of immigration when she was Britain's interior minister, said her aim was to make sure those people from EU countries who had made their homes in her country could stay. She added she would spell out the details of her plan on Monday.
"I remain of the view that this is a fair and serious offer and let's be clear about what we're saying: those citizens from EU countries that have come to the United Kingdom and made their lives and homes in the United Kingdom will be able to stay and we will guarantee their rights in the United Kingdom," she told a news conference at the summit in Brussels.
"I think that's a very serious offer. There are some differences between that and the proposals of the European Commission but the matter will now go into the negotiations."
European Council President Donald Tusk said his first impression of the offer was that it fell short of expectations, while others said they would have to look at the details before determining whether the proposal reduced EU citizens' rights.
The size of the gap between the British and EU positions on what had been viewed as one of the less problematic areas of contention underlines how complicated the negotiations to unravel more than 40 years of union will be.
But May suggested differences were to be expected in the early days of the talks, which will run until March 2019.
"We've had a good constructive start and want to continue the negotiations exactly in that way and that is what we will be doing," she said.
RECRIMINATIONS AT HOME
Several EU officials suggested that May's weakness after her failed gamble in calling the election could boost their chances of forcing more compromise from the British team, a lack of strength only highlighted by recriminations at home.
Her former colleague, finance minister-turned-newspaper editor George Osborne, embarrassed the prime minister when an editorial in his newspaper reported that May had thwarted attempts by her predecessor to give EU citizens living in Britain unilateral guarantees.
"David Cameron wanted to reassure EU citizens they would be allowed to stay. All his cabinet agreed with that unilateral offer, except his Home Secretary, Mrs May, who insisted on blocking it," the Evening Standard reported.
May struck back, saying: "That's certainly not my recollection", but with Conservative lawmakers blaming her personally for leading them into an election in which they lost seats, her position is perilous.
Lawmakers say she will stay on for now, and May's aides were clear that the message she brought to Brussels was that she planned to lead Britain during the Brexit negotiations.
"As I have made clear to my European colleagues, if you look at what happened in the general election, over 80 percent of voters voted for parties who were committed to the United Kingdom leaving the European Union" she said.
"And that is exactly what we are going to do."
(Editing by Andrew Roche)