* Union plans protest marches, picketing
* NUMSA rejected latest pay offer on Sunday
* Strike has forced Toyota, GM, Ford to halt production (changes dateline, adds details)
CAPE TOWN, July 16 (Reuters) - South Africa's main manufacturing union, NUMSA, said it has agreed a plan of action to intensify a three-week strike over pay that has hit car makers and construction companies.
Around 220,000 workers have downed tools in demand of a double-digit wage increase, a blow to Africa's most advanced economy as it struggles to avoid recession and is still recovering from a crippling five-month strike in the platinum sector, which ended in June.
The National Union of Metalworkers of South Africa (NUMSA) rejected a pay offer from employers on Sunday and said on Wednesday that it would immediately start mobilising workers for protest marches across the country. It also plans to hold lunch-time pickets and demonstrations in the auto, rubber, tyre and power sectors.
"The National Strike Committee ... has developed a maximum programme of action to intensify and accelerate the strike action," NUMSA said in a statement on Wednesday.
On Tuesday, employers in the metals and engineering sector withdrew their offer of a 10 percent annual wage increase this year, 9.5 percent in 2015 and 9 percent the following year, after NUMSA rejected it.
The strike has disrupted the supply of components to automobile makers, pushing Toyota, General Motors and Ford to halt production at their assembly plants in South Africa.
Workers participating in the strike also include those from construction companies developing a new state coal-fired power station, Medupi, as well as workers from packaging company Nampak.
Public Enterprises Minister Lynne Brown, however, said on Wednesday that the strike would not affect the start of operations at the power station, which is slated for December.
As well as wage increases, the strike is also about labour issues, including third-party hiring and contract workers, and housing allowances.
NUMSA also wants any deal to be limited to one year while employers, who said they would take their fight to the bargaining council, are keen to lock in a multi-year agreement. (Reporting by Wendell Roelf; Editing by Susan Fenton)