WASHINGTON - President Barack Obama said Tuesday he will announce a new U.S. strategy for Afghanistan soon and that his intention will be to have a plan to finish the job there after eight years of war.

Obama, at a joint news conference with Indian Prime Minister Manmohan Singh, spoke a day after his final meeting with his war council about his new strategy.

Influential voices in Obama's national security cabinet, including Defense Secretary Robert Gates and military chiefs, favor a U.S. troop increase of 30,000-plus, officials said. The final number could reach 35,000 once U.S. trainers are factored in, but estimates on the number of trainers vary widely.

Obama would not be drawn out on specifics but said he would have an announcement after this week's Thanksgiving holiday. He is expected to give a prime-time address next Tuesday.

I will be making an announcement to the American people about how we intend to move forward. I will be doing so shortly, he said.

Noting that the Afghanistan war has been going on for eight years, Obama said it is my intention to finish the job there.

Under pressure from Democrats and many Americans to find a way out of Afghanistan, Obama said it is going to be important to recognize that the Afghan people are ultimately going to have to provide for their own security.

He said he will discuss in his strategy a clear rationale for what the United States is doing in Afghanistan and will say how Afghan security forces can be trained and equipped.

(Additional reporting by Andy Sullivan, Kim Dixon, and Caren Bohan; Editing by Sandra Maler)