WASHINGTON — The United States imposed new sanctions Friday on about two dozen Russians accused of human rights violations, and Moscow vowed to retaliate as a fractious dispute between the two countries escalated further into a cold war-style, tit-for-tat clash.

The Obama administration barred 18 Russians from traveling to the United States and froze any assets they may have here under a new law intended to punish human rights violations. A handful of other more highly placed officials, including the head of the Russian region of Chechnya, were put on a list not publicly revealed. Russian officials promised to ban a like number of Americans.

The back and forth was reminiscent of the days when the two powers expelled equivalent numbers of diplomats to disrupt spy rings or signal displeasure, underscoring the depth of discontent just four years after President Obama resolved to reset the relationship. The dispute has already resulted in Moscow shutting down American adoptions of Russian orphans. The new sanctions came just days before Mr. Obama’s national security adviser, Tom Donilon, travels to Moscow to try to smooth over the tension.

The public sanctions targeted largely midlevel officials but the classified list included Ramzan A. Kadyrov, the president of Chechnya, a Kremlin ally known as a ruthless ruler, according to people briefed on the list. Others on the secret list were figures of such prominence in Russia that the administration feared identifying them might invite retaliation by President Vladimir V. Putin against similarly situated American officials like members of Congress.