In her last major speech before she quits Downing Street next week, Mrs May said there had been a "coarsening" of debate which could be pushing the country to a "much darker place".
Mrs May said: "Today, an inability to combine principles with pragmatism and make a compromise when required seems to have driven our whole political discourse down the wrong path.
"It has led to what is, in effect, a form of absolutism. One which believes that if you simply assert your view loud enough and long enough you will get your way in the end.
"Or that mobilising your own faction is more important than bringing others with you. This is coarsening our public debate."
Speaking at Chatham House in London, Mrs May said: "Some are losing the ability to disagree without demeaning the views of others.
"This descent of our debate into rancour and tribal bitterness, and in some cases even vile abuse at a criminal level, is corrosive to the democratic values which we should all be seeking to uphold."
The PM added: "Words have consequences. And ill words that go unchallenged are the first step on a continuum to ill deeds.
"Towards a much darker place where hatred and prejudice drive not only what people say, but also what they do."
Mrs May insisted there were grounds for concern "both domestically and internationally, in substance and in tone, I'm worried about the state of politics".
She said: "That worry stems from a conviction that the values on which all of our successes have been founded cannot be taken for granted."
And in what some are likely to see as a thinly-veiled rebuke of US President Donald Trump's style, the PM said: "This absolutism is not confined to British politics.
"It festers in politics all across the world. We see it in the rise of political parties on the far-left and far-right in Europe and beyond.
"And we see it in the increasingly adversarial nature of international relations, which some view as a zero sum game where one country can only gain if others lose.
"And where power, unconstrained by rules, is the only currency of value.
"This absolutism at home and abroad is the opposite of politics at its best.
"It refuses to accept that other points of view are reasonable. It ascribes bad motives to those taking those different views."
Mrs May said the only way to resolve the Brexit impasse was to deliver on the referendum result, insisting there is "no greater regret for me than that I could not do so".
She continued: "But whatever path we take must be sustainable for the long term - so that delivering Brexit brings our country back together. That has to mean some kind of compromise."