(Adds fact offer will extend to smaller bondholders)

By Daniel Bases and Sarah Marsh

NEW YORK/BUENOS AIRES, Jan 13 (Reuters) - Argentina will propose a solution to its long-running legal battle with U.S. creditors over unpaid debt to a U.S. court-appointed mediator by the week of Jan. 25, the finance ministry said on Wednesday.

Solving the more than decade-long debt battle would enable Argentina to return to global credit markets and could mark the start of a new wave of investment in Latin America's third-largest economy, kickstarting growth.

"Then we will recommend a new date for us to all sit down and discuss the proposal," Finance Secretary Luis Caputo told reporters after holding his first face-to-face meeting in New York with the creditors suing Argentina over debt it defaulted on in 2002.

Caputo said he met with the main litigants such as Elliott Management Corp's NML Capital Ltd as well as smaller ones known as the "me-too" bondholders. Argentina's offer would include all of them, he said.

In a separate statement, the finance ministry said it expected the creditors to submit their own proposal for negotiations at the same time.

Earlier in the day, Finance Minister Alfonso Prat-Gay told a news conference in Buenos Aires it was in Argentina's interests to reach a deal. The previous government's failure to do so had cost the economy, he said, with creditor claims in New York having risen to $9.9 billion from $2.943 billion originally.

Former President Cristina Fernandez had refused to settle with the hedge funds like NML Capital Ltd that bought Argentine bonds on the cheap after its massive 2002 default and then held out for better terms when Argentina restructured its debt.

They are broadly known in Argentina as "vultures" for picking on the carcass of the economy after the default plunged millions of Argentines into poverty. Not all the holdouts bought their bonds on the cheap however.

In addition to the debt battle, Argentina's new center-right government, which took office in December, also inherited a primary fiscal deficit of 5.8 percent of GDP in 2015, Prat-Gay said.

"The primary fiscal deficit is at its highest in 30 years," he said. Fernandez's two terms were characterized by heavy government spending that aimed to boost the domestic economy.

The new government aims to reduce this deficit to 4.8 percent of GDP this year and 3.3 percent in 2017, in part by eliminating subsidies for public services for the 30 percent to 40 percent of wealthiest Argentines, Prat-Gay said. Subsidies would be maintained for those who needed them, he added.