Previously, South Korean forces were allowed to respond only in kind — if the North fired artillery, the South could answer only with artillery — to contain any dispute. Now, officials said, the military would be allowed to use greater force.

Mr. Lee’s response to this week’s artillery attack is not the first time he has been criticized for sitting on his hands in the face of a deadly provocation by the North. Two years ago, when a South Korean tourist was shot by a sentry at a North Korean mountain resort, his government’s response amounted to a slap on the wrist: suspending tours to the resort and banning South Korean civic groups from visiting the North.

But the clearest case was Mr. Lee’s response in March to the sinking of a South Korean warship, the Cheonan.

Mr. Lee at first seemed to stall by waiting for the results of an international investigation, which took two months to conclude that the ship had been sunk by a North Korean torpedo. When he responded, it was with relatively mild measures like reducing the South’s already minuscule trade with the North, resuming the South’s cold-war-era propaganda speakers along the demilitarized zone and demanding an apology. But the speakers have yet to be turned on after North Korea threatened to shoot at them, and Mr. Lee dropped the apology demand as a condition for talks.

Mr. Lee was widely blamed in South Korea for having provoked the Cheonan episode by ending unconditional aid to the North at the start of his presidency.

“Before, the public saw him as too hard, and now they see him as too soft,” said Yoo Ho-yeol, a professor of North Korean studies at Korea University in Seoul.

Despite public pressure to do more, Mr. Lee does not have many options for less lethal forms of pressure on the North, diplomatic or economic. North Korea has weathered years of economic sanctions and diplomatic isolation. In fact, the tough economic conditions appear only to give the North motivation to continue its brinkmanship, to extract aid as it faces a winter of food and fuel shortages.