The Dutch prime minister, Mark Rutte, said there are "thousands of questions to ask" about May's proposals, and questioned why the British leader was laying them out with European Union leaders instead of with the Brexit negotiators.
The UK expects that the European Union side will compromise on this point.
Under the agreed structure talks about trade would follow the earlier tranche of negotiations, not be held in parallel, as previously requested by the UK.
As recently as last week the government had insisted that trade talks could take place at the same time as discussion of citizens' rights, the Northern Irish border, and financial settlements.
The UK, however, seems unwavering regarding the already announced plans to end the current agreements with the Union and to establish new ones meant to allow a more open relationship with other countries of the world.
In their June 2016 referendum, the majority of the British citizens voted in favor of Brexit (51.9% to 48.1%).
"And of course when it comes to issues relating to the border.it'll be hard to determine the final shape of that until we know what the new trade arrangements are between the United Kingdom and the EU".
Macron won office as a committed European and has joined forces with German Chancellor Angela Merkel pledging to put the EU back on track to deliver prosperity and security after years of austerity and crisis.
It will be their first meeting since her Conservative party unexpectedly lost its majority in a June 8 election, leaving her in charge of a so-called "zombie government".
Brexit negotiations begin after almost a whole year of speculation and build up.
Hours after arriving in Brussels to kick off the first day of the talks on Monday, UK Brexit Secretary David Davis agreed to settle the divorce terms before getting to the details about future relations with the EU.
Another British official said May would offer "new elements" in a paper to be published next week.
Brussels officials said they wanted to hear "what is actually the situation" surrounding the UK's departure from the bloc when the PM addresses her 27 counterparts at a tense EU Council meeting in the Belgian capital tomorrow.
"This first session was useful to start off on the right foot".
David Davis began negotiations yesterday.
This would provide a "smooth path" from "where we are now" to where the United Kingdom would end up post-Brexit, he said.
Tusk said leaders were all deeply concerned by the issue and agreed that if social media companies could not help prevent online radicalisation and hate-crime, then they were ready to introduce legislation to make them do so.
"There is a long way to go, but we are off to a promising start".
Promising details on Monday, May also said those European Union citizens who had lived in Britain for five years could stay for life. "They did vote to leave the EU".
The UK has made a major concession on the first day of Brexit talks, accepting that a trade deal can only be discussed after a multi-billion pound "divorce bill" is settled. A fair deal for both sides was possible, he said.
"You may say I am a dreamer but I'm not the only one", Tusk added, quoting a lyric from the late John Lennon's "Imagine". "It's not about punishment, it is not about revenge", Barnier said.
Health Care gains in danger!!
Senator Roger Wicker of MS expressed some disappointment that the new bill bears too many similarities to Obamacare. The American Academy of Pediatrics, citing the proposed Medicaid cuts, said the bill would hurt children.