He said the best Britain's prime minister could hope for was "further clarity and further interpretations without reopening the withdrawal agreement" when she meets European Union leaders in Brussels this week.
The British leader toured European capitals on Tuesday in an attempt to salvage the deal, after MPs savaged its provisions on the issue of the Irish border.
The Northern Irish party DUP, which is in coalition with the Conservatives, was also left unsatisfied.
Rutte declined to comment on the talks as he arrived at the Catshuis - his official residence in The Hague, by bike for the meeting.
Two Conservative MPs refused to appear on TV together as the party's bitter row over Brexit erupted into a leadership challenge today.
"I doubt if she really knows what she's going to achieve", said Pippa Catterall, professor of history and policy at the University of Westminster.
Even if May wins the votes of more than 50% of the 315 Tory MPs, a close election could still damage her authority.
Meanwhile EU President Donald Tusk said bloc leaders wanted to help the prime minister but added: "The question is how".
Surviving the vote means she would be immune from a further no confidence vote from her party for a year.
Mrs May said securing a Brexit deal which will deliver on the result of the 2016 referendum is "now within our grasp", and added she is "making progress" in securing reassurances from European Union leaders on MPs' concerns about the proposed backstop for the Irish border.
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For the third Saturday in a row, the demonstration in Paris turned violent on the famous Champs-Elysees Avenue, and in other areas of the French capital.
Graham Brady, the chair of the backbench 1922 committee, confirmed that at least 48 MPs had written to him expressing doubts in the Prime Minister. The vote to determine the victor is then opened to the wider Conservative Party membership.
The British parliament will get its vote before January 21, May's spokeswoman said.
After Tory backbenchers chose to "take back control" of their party leadership, they will know that any replacement PM would face the exact same Parliamentary arithmetic and the exact same deadlock over Brexit.
She said she will contest Wednesday's challenge and, if victorious, plans to table a vote on her Brexit deal some time before Jan 21.
With Jeremy Corbyn under pressure from a significant number of MPs and peers to force a confidence vote on the Government, Labour former Cabinet minister Lord Mandelson said the opposition had not laid a glove on the Government.
If May loses, there will be a leadership contest to decide her replacement.
She said: 'Like many people, there are parts of the current deal that I'm uncomfortable with so I'm keen to see if the PM can use the extra time to secure some improvements'.
Former prime minister John Major, who also faced a Conservative revolt over Europe, said Britain must revoke its divorce notice immediately.
She added that she was due to travel to Dublin for further negotiations on Brexit, but would remain in London to make the case for her leadership with colleagues.
"We will put down a motion of no confidence when we judge it most likely to be successful", a party spokesperson said.