For much of the last decade, America’s partisan culture warriors have fought over the contested territory of social media — arguing about whether the rules on Facebook and Twitter were too strict or too lenient, whether YouTube and TikTok censored too much or too little and whether Silicon Valley tech companies were systematically silencing right-wing voices.

Those battles aren’t over. But a new one has already started.

This fight is over artificial intelligence, and whether the outputs of leading A.I. chatbots like ChatGPT, Claude and Gemini are politically biased.

Conservatives have been taking aim at A.I. companies for months. In March, House Republicans subpoenaed a group of leading A.I. developers, probing them for information about whether they colluded with the Biden administration to suppress right-wing speech. And this month, Missouri’s Republican attorney general, Andrew Bailey, opened an investigation into whether Google, Meta, Microsoft and OpenAI are leading a “new wave of censorship” by training their A.I. systems to give biased responses to questions about President Trump.

On Wednesday, Mr. Trump himself joined the fray, issuing an executive order on what he called “woke A.I.”

“Once and for all, we are getting rid of woke,” he said in a speech. “The American people do not want woke Marxist lunacy in the A.I. models, and neither do other countries.”

The order was announced alongside a new White House A.I. action plan that will require A.I. developers that receive federal contracts to ensure that their models’ outputs are “objective and free from top-down ideological bias.”