Mr Weber tweeted: “On rights of EU citizens living in UK, PM May’s proposals are a start, but not enough. More answers needed for these families.
“If PM May cannot come up with a more concrete proposal it is quite worrying for the rest of the Brexit negotiations.”
Earlier in June, he said there was a lack of direction from London about the negotiations and he has said a hard Brexit would be a “disaster” for London.
He said: “We have no indication what they like, what they want to achieve in the negotiations.”
Under Mrs May’s proposals, the EU citizens would have full access to the NHS, education, benefits and pensions.
She said: “This position represents a fair and serious offer – and one aimed at giving as much certainty as possible to citizens who have settled in the UK, building careers and lives, and contributing so much to our society.”
Mr Weber said that Mrs May’s decicision to call a snap General Election caused “chaos” in London.
The head of the EPP has said that the United Kingdom will have to face serious consequences for its decision to leave the Union including loss of status in the economic market.
He said: “I will not, and we, the EPP, will not accept that our currency will continue to be managed there, that they will continue to conduct business with it even though they don’t comply to our banking regulations anymore in Great Britain.”
Mrs May is in Brussels today for the second day of the EU leaders summit and she has said the full detailed proposal of the offer to EU citizens will be made on Monday.
There are more than three million EU citizens living in the UK and Mrs May wants the EU to guarantee the same rights to UK expats in the bloc’s member states.