Data integration from autonomous, remote data sources is complicated by the data source heterogeneity, lack of methodological support and appropriate data integration systems. To solve this problem, the On-demand Remote Data Integration Architecture (ORDIA) is defined, which promotes maintenance and allows minimizing data integration time. A data integration task parallelization algorithm is the key part of this architecture. A detailed description of this algorithm is provided, and its performance is evaluated by experimental comparison with other data integration solutions.