Turqoise Hill shares were last trading at $5.49, 4.8 percent higher on the day.
"There is no doubt that moving forward with the Oyu Tolgoi project will improve the investment climate in Mongolia," Prime Minister Chimediin Saikhanbileg said in a statement.
The project is expected to boost Mongolia's economy by a third when it reaches full capacity.
Disputes between Rio Tinto and Mongolia over taxes and the costs of building the first stage stopped work on the second phase in 2013.
Along with changes in Mongolia's minerals law and the cancellation of 106 mining licenses, the row has deterred foreign investment and worsened the hit to the country's economy from sliding commodity prices, leading the new prime minister to push hard to resolve all the issues.
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The underground expansion, with 25 billion pounds of copper and 12 million ounces of gold reserves, will make Oyu Tolgoi one of the world's top 10 copper mines and propel growth for global miner Rio Tinto outside iron ore.
"This is by far the best undeveloped growth project that any of the majors has, and it's in the best commodity - copper," said Deutsche Bank analyst Paul Young.
Analysts said the underground mine, which Rio says will unlock 80 percent of the copper wealth at the project, could start producing by the end of this decade.
Push for quick start
Under the pact, Rio Tinto agreed to cut its management fees in half to 3 percent of capital costs, gave up a smelter royalty, and agreed to base its 5 percent sales royalty to the government on gross revenue.
Turquoise Hill said those factors were worth less than 2 percent of the $7.4 billon valuation on the underground project.
Before development can begin, Oyu Tolgoi will need to finalise $4 billion in project financing, submit a final feasibility study and secure permits.
The project financing could be completed as early as the fourth quarter, Turquoise Hill Chief Executive Jeffery Tygesen said on a conference call.
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Asked if there was room to reduce the capital cost estimate, Turquoise Hill Chief Financial Officer Steeve Thibeault said the amount remained "substantively what our expectation is".
"The intent for all parties is to move as quickly as we can," Rio Tinto Copper and Coal Chief Executive Jean-Sébastien Jacques told Reuters by phone from Dubai.
He gave no details on how soon Rio Tinto expects to complete a feasibility study but said it would take five to seven years of construction work to reach full capacity.
"It's a big project, and the sooner we start, the better," Jacques said.
Analysts estimate the mine will begin commercial production in 2019 or 2020 at the earliest.