Paratopological groups with a Gδ-diagonal of infinite rank

We present some classes of paratopological groups with a Gδ-diagonal of infinite rank. In particular, we show that every Hausdorff paratopological group with countable π-character has a Gδ-diagonal of infinite rank, which answers a question posed by A. Arhangel'skii and A. Bella. Also, we construct a Hausdorff paratopological group with uncountable π-character which contains a second countable dense subgroup.