* Move will cool expectations of bidding war
* Atlas operates in Australia's iron ore rich Pilbara region
* Fortescue has nearly 20 pct stake in Atlas
(Adds comment, detail; updates prices)
June 20 (Reuters) - Mining infrastructure provider Mineral Resources MIN.AX on Wednesday said it would not make an offer to counter Hancock Prospecting's A$390 million ($288 million) bid for Australia's Atlas Iron AGO.AX .
That will likely cool expectation of a possible bidding war for the iron ore miner, after Atlas on Tuesday gave Mineral Resources three business days to match a A$0.042 per share takeover offer from Australian billionaire Gina Rinehart's Hancock Prospecting.
Atlas operates in the iron ore rich Pilbara region of Western Australia and has undeveloped tenements that could be brought into production with a larger partner.
It also has potential port access coveted by major miners as they look to expand output in coming years, as well as a stake in lithium exports and large tax losses that an acquirer could use to offset their taxable gains.
Hancock Prospecting launched an unconditional all-cash bid for the iron ore miner on Monday, trouncing an earlier A$280.2 million scrip offer in April from Mineral Resources.
The spotlight now shifts to world No. 4 iron ore miner Fortescue FMG.AX which has built up 19.9-percent stake in Atlas - large enough to block Mineral Resources' offer, but not enough to hold back Hancock which is seeking a majority stake.
Fortescue chief executive Elizabeth Gaines said in a statement on Wednesday that the miner would continue to assess its strategic options.
Analyst Peter O'Connor at brokerage Shaw and Partners said the chance of a counterbid by Fortescue was between zero and fifty percent, and suggested the miner was more likely to try to negotiate with Fortescue to carve up Atlas.
If it was not successful, Fortescue may have to "flip the 19.9 percent (Atlas) stake into the Hancock bid, make a couple of shekels profit and move on."
Shares of Atlas Iron were up 2.3 percent, while Mineral Resources shares rose 2.6 percent. The broader Australian market was up 1.2 percent .AXJO .
($1 = 1.3528 Australian dollars)