One month after losing her parliamentary majority in a snap election, the Conservative leader said she was still committed to "bold action" to fulfil her promises of change.
But as fresh rumours swirled of plans to oust her, May accepted that "the reality I now face as prime minister is rather different" than it was.
Her comments came in excerpts of a speech due to be delivered on Tuesday, the anniversary of her winning the Conservative Party leadership race after last year's referendum vote to leave the EU.
"In this new context, it will be even more important to make the case for our policies and our values, and to win the battle of ideas both in parliament as well as in the country," May will say.
"So I say to the other parties in the House of Commons... come forward with your own views and ideas about how we can tackle these challenges as a country."
May has been struggling to maintain her authority since the June 8 election, which she called three years early only to lose seats, leaving her with a minority government.
'Dead in the water'
The Mail on Sunday reported that former Conservative chief whip Andrew Mitchell had told a private meeting of MPs that May was "dead in the water" and must quit.
Justice Secretary David Lidington said this and other rumours were the result of politicians enjoying "too much sun and too much warm Prosecco" at summer parties.
May's de facto deputy Damian Green insisted Monday that her call for cross-party cooperation was a "grown-up way of doing politics".
May had been accused of stifling dissent over her plans to take Britain out of Europe's single market, end jurisdiction of the European Court of Justice, and leave the bloc without a deal in place.
But members of her cabinet have been increasingly outspoken since the election, particularly finance minister Philip Hammond, who favours a more conciliatory approach amid fears of the damage a clean break could do to business.
A new cross-party parliamentary group was launched on Monday calling for the "closest possible relationship" with the EU and demanding that "all options are kept on the table" in the negotiations, which began last month.
It is co-chaired by opposition Labour MP Chuka Umunna and Conservative former minister Anna Soubry, both outspoken pro-Europeans, and backed by the smaller Liberal Democrats.
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