President Trump signed an executive order on Thursday seeking to severely punish the law firm Perkins Coie by stripping its lawyers of security clearances and access to government buildings and officials — a form of payback for its legal work for Democrats during the 2016 presidential campaign.

With the order, Perkins Coie becomes the second such firm to be targeted by the president. Late last month, he signed a similar memorandum attacking Covington & Burling, which has done pro bono legal work for Jack Smith, who as special counsel pursued two separate indictments of Mr. Trump.

While the Covington memorandum sought to strip clearances and contracts from that firm, the Perkins Coie order goes much further, seeking to also limit its lawyers’ access to federal buildings, officials and jobs in a way that could cast a chilling effect over the entire legal profession.

The president’s animosity toward Perkins Coie dates back eight years, to when two lawyers at the firm, Marc Elias and Michael Sussmann, played roles in what eventually became an F.B.I. investigation to determine if anyone on the 2016 Trump presidential campaign conspired with Russian agents to influence the outcome of that election. Both lawyers left that firm years ago.

The executive order denounces what it calls “dishonest and dangerous activity” at Perkins Coie, singling out its hiring of a research firm that led to the compilation of a dossier of unsubstantiated allegations against Mr. Trump related to possible ties between his campaign and Russia. The executive order accused the firm of “undermining democratic elections, the integrity of our courts and honest law enforcement.”

The order instructs federal agencies to suspend any security clearances that Perkins Coie lawyers may have. It also orders government agencies to determine if they have any contracts with the law firm, and then cancel them.

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