Obama yesterday reversed plans to withdraw around 5,000 US troops from Afghanistan this year, an overture to the country's new reform-minded leader, President Ashraf Ghani.
Hosting Ghani at the White House for their first presidential head-to-head, Obama agreed to keep the current level of 9,800 US troops in Afghanistan until the end of 2015.
"Obama's announcement to continue to keep troops in Afghanistan is a response to the peace efforts," Taliban spokesman Zabihullah Mujahid told AFP.
Since coming to power in September after protracted power-sharing negotiations, Ghani has sought to establish a peace process with the Taliban to end their 13-year fight against the Kabul government and its foreign backers.
Supportive signals from Pakistan, which has long held significant influence over the Taliban, have boosted hopes for possible dialogue.
The Taliban, who have waged a bloody insurgency since being toppled from power in 2001 in a US-led invasion, have always denied talks with the government.
They maintain they will not negotiate while foreign troops remain on Afghan soil.
Obama's decision means they will have air and other crucial US support through this year's fighting season, which begins in weeks.
But the militants voiced defiance.
"When there were more than 100,000 troops on the ground, they could not beat us - now with 10,000 they cannot do anything," Mujahid said.