The Trump administration asked states to abstain from releasing unemployment-claims figures prior to the publication of a national compilation of weekly U.S. jobless claims, according to a state labor department official.

The official cited an email sent on Wednesday from Gay Gilbert, an administrator at the U.S. Labor Department. The message, sent as states across the nation started reporting surges in claims tied to the coronavirus pandemic, said jobless claims are closely watched by policy makers and financial markets during...