The Taliban, in a statement, said "at least" seven "invading terrorists" were killed in overnight attacks on Ghazni province.
"As any as seven NATO invading terrorists and their puppets" were killed in Kapisa province during Thursday morning attacks.
However, the NATO-led International Security Assistance Force in Afghanistan, in its Thursday operational update, made no mention of Taliban or coalition casualties.
Obama and Karzai signed a strategic agreement that outlines the U.S. military engagement in Afghanistan after 2014, when international forces are expected to leave the country. Some U.S. troops will stay behind in order to train Afghan forces.
The Taliban, in a series of statements documenting their offensive, added that six members of the Afghan national army in overnight attacks in Paktika province and another six members of an Afghan security team were killed Thursday morning in Ghazni province.
International forces have praised the ability of Afghan forces to take responsibility over some security operations in the country. U.S. and NATO-led forces been accused, however, of overstating the success of their Afghan counterparts.