May gambled that a strong election win, as forecast by some pollsters, would boost her majority in the House of Commons in time for the Brexit talks, but instead, her party surrendered 13 seats in the lower chamber.
The Conservatives are still negotiating with the Democratic Unionist Party over whether their 10 MPs will support the Tories' minority government.
But the Government will press ahead with the first round of Brexit talks two days before the official opening of Parliament.
The Prime Minister has insisted the United Kingdom will leave the single market, replace customs union membership with a new deal and end the jurisdiction of the European Court of Justice. It does not wash.
European Union leaders, who will meet May at a summit next Thursday, have been irritated by her repeated threats to walk out with "no deal" - even if most see that as a campaigning bluff given the chaos it would cause.
"Theresa May must immediately create a cross-party joint Cabinet committee to negotiate Brexit".
The Prime Minister triggered Article 50, the legal process for leaving the European Union, on 29 March.
An EU official close to the matter said the "softer Brexit" talk could be "productive" and help progress in the first months, where the British attitude to discussing the financial settlement "will be the first serious test of the negotiations".
The first round of talks are likely to focus on the UK's so-called divorce bill, estimated to be as much as €100bn (£88bn), as well as the rights of European Union citizens now living in Britain and United Kingdom nationals living on the continent.
Brussels has insisted talks on the so-called divorce, taking in issues including the fee the United Kingdom will have to pay to sever its ties, must make sufficient progress before any discussion on a future trade agreement could begin.
If May now sends a team to Brussels - ideally on schedule on Monday - that shows willing on the EU's priority "Phase One" issues, then trade talks could get under way by the turn of the year - a step-by-step timetable Barnier says must be followed to limit the risk of a disruptive "no deal".
The Prime Minister will attend the European Council summit to discuss issues such as migration and security, but will be absent from a dinner when the 27 other national leaders review the start of the Brexit process.
And despite French President Emmanuel Macron stating the United Kingdom could still opt to remain an European Union member, Verhofstadt added this would not mean a return to previous circumstances.