BRASÍLIA—The embattled speaker of Brazil’s lower house of congress said he was opening impeachment procedures against President Dilma Rousseff, setting in motion what is likely to be a bitter and protracted power struggle in a nation already reeling from a deep recession and its worst-ever corruption scandal.

The impeachment request on Wednesday contends that Ms. Rousseff’s administration breached federal accounting laws in 2014 and 2015, a charge the president has repeatedly denied.

Ms....