ALGIERS (Reuters) - Algeria's government has bowed to demands from teachers' unions for a big pay increase after a three-week strike forced thousands of schools to close, a leader of one of the unions involved said on Tuesday.

The strike was the biggest in six years in Algeria, whose government is struggling to keep a lid on inflation and faces its first budget deficit in a decade despite holding large cash reserves from oil and gas exports.

Teachers have complained that they are being forced into poverty and debt because inflation, 5.8 percent according to the International Monetary Fund, has eaten up previous pay rises.

Their complaints are part of a broader pattern of social unrest -- also fuelled by anger over unemployment and poor housing -- that diplomats say is on the increase and could threaten Algeria's stability.

Meziane Meriane, head of an independent union for secondary school teachers, told Reuters the government had agreed to the strikers' main demand -- to backdate a teachers' pay increase to January 2008.

"Thanks to a major mobilisation in the education sector, which has been paralysed for three weeks ... the prime minister has agreed to the back-dating," Meriane said outside the education ministry after a meeting with officials.

The government has not released any figures for the cost of the back-dated rise, but Meriane said it would be "enormous".

Calculations based on the average salary of Algeria's roughly 600,000 teachers suggest the cost of the rise could be over $1 billion. Total government expenditure in this year's budget is the equivalent of $73 billion.

The teachers' success may encourage unions in other sectors to launch strikes of their own. Algerian media reported this week that some unions representing healthcare workers were planning stoppages to demand better pay and conditions.