The deal, signed by both parties in February, saw the US and Nato agree to withdraw all troops from Afghanistan within 14 months in return for Taliban commitments to prevent terrorism.
But Taliban militants said in a statement they would escalate violence in the region if the US and the Afghan government continued alleged violations of the deal.
The statement said they had restricted attacks against Afghan security forces to rural outposts, had not attacked international forces and had not attacked Afghan forces in cities or military installations.
These limits on their attacks had not been specifically laid out in the agreement with the US, they said.
They also chastised the Afghan government for delaying the release of 5,000 Taliban prisoners promised in the agreement.
US military spokesman Colonel Sonny Leggett denied the Taliban allegation, tweeting that US forces in Afghanistan have “upheld and continues to uphold the military terms of the US-TB (Taliban) agreement; any assertion otherwise is baseless”.
Col Leggett called for Taliban to reduce violence and said the US military will continue to come to the aid of Afghanistan's security forces if attacked, in line with the agreement.
The militants said they had reduced their attacks compared to last year, but warned continued violations would “create an atmosphere of mistrust that will not only damage the agreements, but also force mujaheddin to a similar response and will increase the level of fighting”.
The Taliban have accused the Afghan government of using “indefensible arguments” to explain the repeated delays in releasing a promised 5,000 Taliban prisoners in exchange for 1,000 government personnel.
The Afghan government's foot-dragging has also left Washington frustrated.
Meanwhile, in the Afghan capital, president Ashraf Ghani announced his new cabinet even as he squabbles with his main political challenger over last year's election results.
Mr Ghani's move came even as mediators, including former president Hamid Karzai, shuttled between the president and his opponent, chief executive Abdullah Abdullah, who has also declared himself Afghanistan's president.
The country's independent election commission has declared Mr Ghani a winner, but Mr Abdullah and the Elections Complaint Commission have charged widespread irregularities.
Attempts to negotiate an end to the political turmoil in Kabul have made little progress, frustrating the US and potentially derailing the next stage in the Afghan peace process.
Washington has threatened to withhold $1bn in aid this year if Mr Ghani and Mr Abdullah cannot reach a compromise.
The Trump administration wants a quick start to intra-Afghan negotiations, the next step in the peace deal it signed on 29 February.
It looked promising when Mr Ghani announced his negotiating team last week, but Mr Abdullah's response to it has been lukewarm and the Taliban have rejected it as one-sided.
The US and Nato have already begun to withdraw troops from Afghanistan.
The full withdrawal is expected to be completed in 14 months and is tied to Taliban commitments to fight terrorist groups and help in the battle against Isis.
The withdrawal is not tied to the success of intra-Afghan negotiations, but US secretary of state Mike Pompeo had travelled to Afghanistan last month to try to break the impasse between Mr Ghani and Mr Abdullah.
Mr Pompeo left without a solution, but last week he welcomed that the Afghan government had put together a negotiating team and made progress towards the prisoner releases.
Those releases have stumbled even as the Taliban sent a three-member team to Kabul last week.
Additional reporting by AP
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