DAVOS, Switzerland — Afghanistan is prepared for a major reduction in United States forces there, President Ashraf Ghani said on Thursday, adding that he had given that message to President Trump, a step toward winding down the costly American military presence as diplomats struggle to finalize a peace deal with the Taliban.

About 12,000 American troops remain in Afghanistan, down from a peak of about 100,000 eight years ago. The eventual withdrawal of those forces has been one of the strongest pieces of leverage American negotiators have in talks with the Taliban to end the 18-year war.

A gradual reduction in United States troops in the country has taken place over the last year, despite the absence of a settlement emerging from peace negotiations in the Gulf state of Qatar over the past year. Mr. Trump declared the talks “dead” in September, just as the two sides were on the verge of finalizing an agreement. They later resumed, but have since stalled.

Mr. Ghani has been a vocal critic of the United States’ negotiations with the insurgents, because the talks have excluded his government. But speaking on the sidelines of the World Economic Forum in Davos, Switzerland, on Thursday, he said he had told Mr. Trump that the Afghan government was ready for a further reduction of 4,000 American troops, one-third of those remaining.