BOGOTÁ—Colombian President Juan Manuel Santos ordered army troops into the capital Friday to keep the peace after violent street protests that left two dead, as the government toughens its position in a farmer-led nationwide strike that began nearly two weeks ago.

The president said as many as 50,000 troops were set to be deployed in Bogotá and on highways around the country following the violent protests that rocked the city's downtown area Thursday as university students and other city dwellers came out to support the demands...