By Peter Evans

LONDON--British American Tobacco PLC Wednesday said smokers around the world continued to feel pressure on their disposable income, resulting in a big fall in first-quarter revenue and sales volumes.

The maker of Lucky Strike, Dunhill and Kent cigarettes said revenue declined 5.8% in the three months to March 30, compared with a fall of 12% in the same period a year earlier. Revenue increased 1.7% when the impact of currency movements was stripped out, BAT said.

Cigarette volumes fell 3.6%, somewhat worse than the 1.4% decline reported in 2014. Volumes in Brazil, Russia and Vietnam had been hit especially hard, BAT said. The company added that it had offset much of the fall in volumes by raising prices across many of its biggest markets.

"I remain confident that we will deliver another good year of earnings growth at constant rates of exchange," Chief Executive Officer Nicandro Durante said.

Write to Peter Evans at peter.evans@wsj.com