WASHINGTON—U.S. officials are discussing whether to respond to computer breaches of Democratic Party organizations with economic sanctions against Russia, but they haven’t reached a decision about how to proceed, according to several people familiar with the matter.

Levying sanctions would require the White House to publicly accuse Russia, or Russian-backed hackers, of committing the breach and then leaking embarrassing information. The U.S. has frequently opted not to publicly release attribution for cyber-assaults, though Washington did openly accuse North Korea of carrying out an embarrassing breach of Sony Pictures Entertainment Inc. in 2014.

The Federal Bureau of Investigation and U.S. intelligence agencies have been studying the Democratic hacks, and several officials have signaled it was almost certainly carried out by Russian-affiliated hackers. Russia has denied any involvement, but several cybersecurity companies have also released reports tying the breach to Russian hackers.

On Thursday, House Minority Leader Nancy Pelosi (D., Calif.) told reporters, regarding a breach of the Democratic Congressional Campaign Committee, which spearheads the Democratic House campaigns: “I know for sure it is the Russians” and “we are assessing the damage.”

She added, “This is an electronic Watergate…The Russians broke in. Who did they give the information to? I don’t know. Who dumped it? I don’t know.”