Ship owners are stepping up pressure on governments world-wide to take a stronger role in policing the waters off Somalia and prosecuting hijackers, saying lax enforcement is encouraging attacks and helping pirates extend their operations farther into the Indian Ocean.

Piracy hit an all-time high in the first three months of 2011, with 142 attacks world-wide, up from 67 a year earlier, according to statistics from the International Maritime Bureau, a non-profit organization set up to counter maritime crime. The sharp increase...