A valve assembly can include a generally tubular housing, a mandrel reciprocably disposed in the housing and operative to displace a valve closure in response to relative displacement between the mandrel and the housing, an engagement device reciprocably disposed externally on the housing and secured relative to the mandrel, so that the mandrel displaces with the engagement device, and a biasing device that biases the mandrel and engagement device in a selected longitudinal direction. A system can include a tubular string and a valve assembly reciprocably disposed in the tubular string, the valve assembly including a valve that selectively restricts flow through a longitudinal passage. The valve closes in response to displacement of the valve assembly in a selected longitudinal direction relative to the tubular string, and the valve opens in response to displacement of the valve assembly in the same longitudinal direction relative to the tubular string.