A day after the Venezuelan opposition’s call for a military uprising failed, the country’s political crisis returned to a protracted standoff punctuated by violence on Wednesday, with the government and protesters seeking to project strength at rival May Day rallies.

“There’s no turning back,” Juan Guaidó, the opposition leader, told supporters in Caracas, the capital, where tear gas fired by riot police officers shrouded some protest sites. “Despite the repression, we’re still here.”

There were reports late in the day that armed pro-government forces used live fire against some protesters in Altamira, part of a Caracas area where the opposition is strong. A 27-year-old woman died from a gunshot wound to the head while protesting there, according to local rights groups.

Thousands of Mr. Guaidó’s supporters in Caracas and elsewhere heeded his call to demonstrate, although not enough to meet his promise to stage “the biggest march in history.” Still, his ability to remain at large and to rally supporters — after his attempt to recruit the military to his side sputtered on Tuesday — underlined the weaknesses in the government of his opponent, President Nicolás Maduro.