In a partially reconfigurable FPGA of the future, arbitrary portions of its logic resources and interconnection networks will be reconfigured without affecting the other parts. Multiple tasks will be mapped and executed concurrently in such an FPGA. Efficient execution of the tasks using the limited resources of the FPGA will necessitate effective resource management. A number of online FPGA placement methods have recently been proposed for such an FPGA. However, they cannot handle I/O communications of the tasks. Taking such I/O communications into consideration, we introduce a new approach to online FPGA placement. We present an algorithm for placing each arriving task in an empty area so as to complete all the tasks efficiently. We develop two fitting strategies to effectively handle I/O communications of the tasks. Our experimental results show that properly weighted combinations of these and two other previously proposed strategies enable this algorithm to run very fast and make an effective placement of the tasks. In fact, we show that the overhead associated with the use of this algorithm is negligible as compared to the total execution time of the tasks.