(Adds comment from President Kirchner, details)

By Cesar Illiano

BUENOS AIRES, April 9 (Reuters) - Argentine schoolteachers went on a one-day nationwide strike on Monday after a high school chemistry teacher was killed by police last week during a protest over pay.

In the capital, Buenos Aires, workers at banks, hospitals, government offices, and public transportation joined the strike for one hour.

Carlos Fuentealba, a 41-year-old teacher, died on Thursday, a day after he was hit in the head by a tear gas cartridge when police broke up a teachers' protest and roadblock in the southern province of Neuquen.

Many protesters blame the teacher's death on Neuquen Gov. Jorge Sobisch, who ordered police to break up the blockades and marches.

"Professor Carlos Fuentealba's assassin has a name. His name is Sobisch, and he must pay. He must go, he must answer for his crimes," Hugo Yasky, president of the national teachers' union, said at a rally in Buenos Aires.

In the northern city of Salta, police fired tear gas at protesting teachers who broke off from a larger group and tried to enter the provincial legislature by force, local TV showed.

Center-left President Nestor Kirchner criticized the killing of Fuentealba, reiterating his stance that the police should not crack down on street protests.

"We strongly reject violence and, of course, those of us in the state must exercise with great responsibility the monopoly we have on security, particularly in these kinds of protests," Kirchner said.

"I will always act in favor of co-existence, even if it means they call me permissive."

The teacher's death has complicated Sobisch's presidential bid to unseat the popular Kirchner in October. Recent polls showed Sobisch with support in the single digits.

The protest in Neuquen last week came after many provinces said they do not have enough money to give teachers raises decreed by the central government.

A February government decree raised base salaries for Argentine teachers by 24 percent. Inflation last year was close to 10 percent and the base teacher's wage was raised to about $334 from $270 a month, which was below the poverty level for a four-person family.

In Neuquen on Monday, teachers painted the doors and windows of the provincial government building black. Signs posted throughout the city of Neuquen lambasted Sobisch, calling him a murderer and the enemy of workers.

The Patagonian province's teachers' union threatened to camp out in front of the government building until Sobisch replaced his education and justice ministers.

"They shot Carlos, but they shot not only him, they shot my entire family, and they also shot all those things he stood for," his widow, Sandra Rodriguez, told reporters. (Additional reporting by Damian Wroclavsky)

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