The global mining giant said on Wednesday it now holds 49.49 percent of Riversdale, a Mozambique-focused coal miner, clearing the 47 percent target it had set itself and raising the price of the deal to A$16.50 a share.
The higher price depended on Rio getting to at least a 47 percent stake in Riversdale by late on April 6, otherwise it would have paid A$16 a share.
Rio's offer, announced in December, was originally conditional on at least 50 percent acceptances, but it was forced to revise that plan last week after Riversdale's other two top shareholders, Brazilian steel CSN
Rio has since said it would go ahead even with a minority stake.
CSN, Brazil's biggest steel maker, has said it has no immediate plans to sell its stake in Riversdale because it sees the asset as strategic -- selling the holding would lessen its bargaining power to control coal supplies.
CSN owns 19.9 percent of Riversdale, while Tata, the world's seventh-largest steelmaker, recently increased its stake in the Australian-listed company to 27 percent.
Rio has targeted Riversdale because of its hard coking coal projects in Mozambique, which could eventually supply as much as a tenth of the global market for the key steel-making ingredient.
The bid fits with Rio's strategy of developing large, long-life, low-cost assets, as China and India fuel demand for African coking coal. Reconstruction activities in Japan are likely to increase demand still further.
But the tussle for Riversdale has shown that even miners targeting smaller, bolt-on acquisitions to make use of their cash piles can encounter problems in deals that pit producers against commodity consumers as prices rise.
Coal prices have seen sharp spikes since December in response to floods in Australia, Japan's disaster and Germany's decision to shut 7 megawatts of nuclear power.
Earlier on Wednesday Rio announced a 46.78 percent holding. It had been expected to hit its 47 percent target with the help of passive index funds, who sold their shares into the offer.
The offer price increase has also triggered an extension of the offer period until April 20.
Rio's London shares were trading up 0.5 percent at 4,434 pence at 1035 GMT.
(Reporting by Clara Ferreira-Marques; Editing by Julie Crust and Will Waterman)