Unions representing about 1.3 million South African state workers and the government have narrowed differences on a wage deal, nearing a settlement on pay rises that could add more than $1 billion to budget spending.A union official said on Tuesday the government had offered a three-year deal with a 6.7 percent increase for this year, with second year increases of inflation plus 0.7 percent and third year increases of inflation plus 0.5 percent."Negotiations seem to be back on track,” said Chris Klopper, spokesman for the Independent Labour Caucus, one of the more than a dozen unions in contract talks with the government.Talks over pay increases broke down last week, raising the threat of a strike that could shut hospitals and schools. The government had offered a 6.5 percent wage increase this year while unions were looking for a figure over 7 percent.Public services minister Lindiwe Sisulu said last week the 6.5 percent offer would swell spending and cost the government about 10 billion rand more than had already been set side.Wages for government employees are the largest sector of state spending, equivalent to more than 40 percent of tax revenue. A perk to provide civil servants with about $100 a month to help them with housing ends up costing South Africa as much each year as its court system.Union officials said the government is looking to cut the amount it spends for housing allowances, which could pose a stumbling block.