June 5 (Reuters) - A months-long dispute between Trump administration officials and AI firm Anthropic is showing signs of easing across parts of the U.S. government as the company prepares to go public, according to sources familiar with the relationship. 

The relationship ruptured earlier this year after Anthropic refused to allow the U.S. military to use its AI models for domestic surveillance and fully autonomous weapons systems, and the government retaliated by putting it on a national security blacklist, set to take effect later in the year. 

The Defense Department in March labeled the company a "supply-chain risk," the first time a U.S. company received the designation, normally reserved for companies tied to adversarial nations. The label bars tens of thousands of contractors from using Anthropic's AI when working for the U.S. military.

The relationship has improved since Anthropic CEO Dario Amodei visited the White House in mid-April to discuss working together for the ‌first time since the dispute erupted, even though Anthropic is still challenging the supply-chain risk designation in court.

The Department of Defense is still "vigorously" defending itself against Anthropic's lawsuit, said Franklin Turner, an attorney specializing in government contracts. Any broader damage to the company's business is unlikely to ease until the department's dispute with the company is resolved, he said. 

"Anytime the government signals that it's washing its hands of a company, that's a major problem for that company," Turner said.

One of the biggest signs of a thaw was symbolic but important. The White House invited Amodei to Trump's planned May 21 signing of an executive order on artificial intelligence, according to two sources familiar with the matter, though the event was later canceled because of Trump's dislike of some of the order's provisions.

Trump signed the order on Tuesday; Anthropic in a statement posted on X said it looked forward to "collaborating" with the White House on implementing the order. 

A White House spokesperson did not respond to a request for comment about the administration's relationship with Anthropic.

Anthropic's press team declined to comment.

DISCUSSIONS WITH OTHER OFFICIALS

Anthropic has held discussions with National Cyber Director Sean Cairncross about Mythos, its most advanced AI system, and how to protect critical infrastructure from AI-enabled cyberattacks, according to a person familiar with the matter. The company has warned that Mythos could supercharge such attacks.

Critical infrastructure refers to vital U.S. economic sectors deserving ​of special protection from ⁠attacks, such as banks, emergency services and hospitals.

Anthropic's relationship with the Trump administration is warming as it gears up for a stock-market debut that could value it at $1 trillion. CEOs of large corporations have tried to bolster relationships with the White House to avoid Trump's anger.

Stronger ties could help bolster investor confidence in the short term, said Harrison Rolfes, a senior research analyst at PitchBook who covers AI companies.

It's a "near-term bruise," Rolfes said, referring to the dispute. 

Anthropic employees met with U.S. Treasury Secretary Scott Bessent this spring to talk about Mythos and potential presidential actions on AI, according to a U.S. official. The discussions helped Trump's team develop June 2's executive order, according to the official, where Trump asked leading developers to hand over their most advanced models for cybersecurity testing.

The tensions with the Pentagon have not faded entirely. Both sides were still arguing over the supply-chain risk designation as of Thursday, when they submitted briefs to the court.

At the same time, Anthropic employees were not part of an April 27 Army-run AI simulation on cyberattacks, according to Army spokesperson Sean Minton, which included cyber executives from leading AI developers including Google and OpenAI, according to an Army statement.