The declaration comes a day after President Ashraf Ghani said he would continue the partial truce at least until talks between Afghan officials and the Taliban kick-off, supposedly on March 10.
The Taliban said on Monday they were resuming offensive operations against Afghan security forces, ending the partial truce that preceded the signing of a deal between the insurgents and Washington.
The declaration comes only a day after President Ashraf Ghani said he would continue the partial truce at least until talks between Afghan officials and the Taliban kick-off, supposedly on March 10.
It ran for one week ahead of the signing of the historic accord in Doha on Saturday and continued over the weekend.
"The reduction in violence... has ended now and our operations will continue as normal," Taliban spokesman Zabihullah Mujahid said.
"As per the (US-Taliban) agreement, our mujahideen will not attack foreign forces but our operations will continue against the Kabul administration forces."
He said the Taliban will not take part in intra-Afghan talks until about 5,000 of their prisoners are released, presenting a major possible barrier to ending the war.
The agreement calls for up to 5,000 jailed Taliban prisoners to be released in exchange for up to 1,000 Afghan government captives by March 10.
"The Afghan government has not made any commitment to release 5,000 Taliban prisoners before the start of any potential negotiation," Sediq Sediqqi, a spokesman for Ghani, said in response to the Taliban's statements.
Fawad Aman, deputy spokesman for the defence ministry said the government was "checking to see if (the truce) had ended".
"We have not had any reports of any big attacks in the country yet", he added.
Since the deal signing on Saturday, the Taliban have been publicly celebrating their "victory" over the US.
Under the terms of the deal, foreign forces will quit Afghanistan within 14 months, subject to Taliban security guarantees and a pledge by the insurgents to hold talks with the Kabul government.
The dramatic fall in attacks due to last week's partial truce between the Taliban, US and Afghan forces offered Afghans a rare opportunity to go about their daily lives without fear of violence.
Bomb attack at a football match
A bombing at a football match killed three people and injured 11 others on Monday in eastern Afghanistan, a police official said.
No group immediately claimed responsibility for the attack.
"A motorcycle rigged with a bomb exploded during a football match," said Sayed Ahmad Babazai, police chief of eastern Khost province, giving details of the toll.