CHICAGO — Chicago and two major airlines have reached a nearly $1.2 billion agreement that resolves many disagreements over the expansion of O’Hare International Airport.

That means construction of an additional runway can begin soon, though questions about timing of other planned work still must be ironed out.

Improving O’Hare will not only reduce flight delays and improve service, “it will ensure one of our busiest airports continues to thrive economically in the future,’’ Transportation Secretary Ray LaHood said.

United and American had filed a lawsuit accusing the city of violating a lease agreement giving airlines authority to approve expenditures for capital projects. Mayor Richard Daley said the airlines had reneged on a 2001 promise to help overhaul O’Hare, which is expected to have a final price tag of around $15 billion.

The March 14 statement did not break down how much of the bill each airline agreed to pay. Nor was it clear if the deal put the brakes on litigation. But American Airlines chief executive Gerard Arpey hailed the agreement, saying it takes into account economic realities.

Mayor-elect Rahm Emanuel, who has supported O’Hare expansion, welcomed the deal, calling it “a victory for the economic future of our city, our state, and our region.’’

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