The UK prime minister - who likewise promised to convey Brexit "on time" - was talking after a progression of gatherings with best EU authorities in Brussels.
European Commission President Jean-Claude Juncker again discounted the sort of changes Mrs. May needs to see.
Mrs. May said she had additionally addressed European Council President Donald Tusk about his remarks on Wednesday about there being a "unique spot in damnation" for the individuals who battled for Brexit without an arrangement to convey it securely.
She said Mr. Tusk's language "was not useful" and had "caused across the board frighten in the United Kingdom".
Mrs. May said she had revealed to him he ought to be "focusing" on working with the UK to get a Brexit bargain.
Mr. Tusk tweeted that there was "no breakthrough in sight" following his discussions with the UK prime minister.
Mrs. May also said that she has "set out very clearly the position from Parliament that we must have legally binding changes to the withdrawal agreement in order to deal with Parliament's concerns over the backstop".
She said that that was together with the other work that we're doing on specialists' rights and different issues, will convey a steady dominant part in Parliament.
Mr. Juncker "underlined that the EU27 will not reopen the withdrawal agreement" in their discussions, as indicated by a joint explanation discharged by the opposite sides.
Yet, he "communicated his receptiveness" to adding words to the non-restricting future relationship archive - that likewise must be upheld by MPs - to be "progressively eager as far as substance and speed".
In the meantime, Brexit Secretary Steve Barclay and EU moderator Michel Barnier will hold talks in Strasbourg on Monday, as the EU and UK Brexit negotiating groups examine proposed changes to the arrangement.
Downing Street said these talks would cover "alternative arrangements" for the Irish border, as called for by MPs in a vote last week.
A representative said other UK ministers, for example, Attorney General Geoffrey Cox could be included.
Mr. Cox is “working on working on possible ways in which legal texts could be drafted, that gave effect to the objective we want," Cabinet Office Minister David Lidington told the BBC.
Mrs. May and Mr. Juncker will meet again before the finish of February, to survey advance.
The prime minister is required to put the arrangement to a vote in the Commons towards the finish of February.
eremy Corbyn has kept in touch with the prime minister setting out his gathering's cost for supporting a Brexit bargain and to offer converses with secure "a sensible agreement that can win the support of Parliament and bring the country together".
The Labor chief's five requests incorporate a "perpetual and thorough UK-wide traditions association" lined up with the EU's traditions controls yet with an assertion that incorporates a UK state on future EU exchange accords.
Mr. Corbyn likewise needs close arrangement with the EU single market and dynamic arrangement on rights and securities for specialists so UK gauges don't fall behind those of the EU.
He likewise proposes cooperation in EU offices and financing projects, and concessions to security and holding access to the European Arrest Warrant.
The letter does not make reference to past requests that any arrangement must convey precisely the same advantage that enrollment of the single market and traditions association as of now does - viably rejecting the gathering's "six tests" that had been its Brexit approach.
The BBC's Political Editor Laura Kuenssberg said Labor's shadow Brexit secretary Sir Keir Starmer would meet Cabinet Office Minister David Lidington to talk about the recommendations.
Yet, the move was met with overwhelm by Labor individuals from the People's Vote battle for another EU submission, who blamed Mr. Corbyn for backpedaling on his responsibility, made at the gathering's meeting, to back an open vote on the off chance that he can't constrain a general decision.
Be that as it may, the move was met with dishearten by Labor individuals from the People's Vote crusade for another EU submission, who blamed Mr. Corbyn for backpedaling on his responsibility, made at the gathering's meeting, to back an open vote on the off chance that he can't drive a general decision.
Work MP Owen Smith, who made a fizzled initiative offer in 2016, has told the BBC he and others were considering stopping the gathering over Mr. Corbyn's Brexit position.
Yet, Labor's Stephen Kinnock, who backs the Norway Plus model of a nearby monetary organization with the EU, invited Mr. Corbyn's letter, tweeting: This can break the gridlock.
Mr. Lidington said he and Brexit Secretary Steve Barclay would examine Labor's proposition with Sir Keir and different frontbenchers.
Be that as it may, he said Labor's call to have a state in economic agreements while being in a traditions association with the EU was unrealistic reasoning, since Brussels had precluded it.
The European Parliament's Brexit coordinator Guy Verhofstadt invited Mr. Corbyn's recommendations, saying the broadest conceivable lion's share was required for a Brexit bargain in the UK and cross-party co-activity is the route forward.
It was likewise supported by Conservative MP Sir Oliver Letwin, who needs to see the UK in a Norway-style association with the EU after Brexit.