US President Trump has 'conditionally approved' a peace deal with the Taliban that may lead to the withdrawal of US troops as long as the Taliban can commit to a reduction in violence, according to a report in the New York Times.

But the deal will "only be signed if the Taliban prove their commitment to a durable reduction of violence over a test period of about seven days later this month," the report said.

If the reduction in violence is upheld, then a US-Taliban agreement is expected to lead to intra-Afghan talks, the Times reported.

On Tuesday, US Secretary of State Mike Pompeo in separate phone conversations with President Ashraf Ghani and Chief Executive Abdullah Abdullah informed both leaders of "progress" in the US-Taliban talks. President Ghani tweeted about his conversation, and Abdullah's office issued a statement.

“Today, I was pleased to receive a call from US Secretary Mike Pompeo, informing me of the notable progress made in the ongoing peace talks with the Taliban. The Secretary informed me about the Taliban’s proposal with regards to bringing a significant and enduring reduction in violence,” Ghani tweeted.

According to a statement from Abdullah's office, the US Secretary of State Mike Pompeo in a phone call Tuesday evening talked with CE Abdullah Abdullah and thanked the CE for his continued cooperation and support for peace efforts and spoke about progress in peace talks between the US and the Taliban.

According to the statement, Pompeo said he hopes that this development will provide the basis for the signing of a bilateral agreement, the start of inter-Afghan negotiations and the achievement of lasting peace.

The US reduced its troop strength in Afghanistan from 15,000 to 13,000 American troops in October, according to reports.

In his State of the Union address earlier this month, Trump vowed he would bring troops home from Afghanistan though he did not offer a timeline.

"In Afghanistan, the determination and valor of our warfighters has allowed us to make tremendous progress, and peace talks are underway," the president said. "I am not looking to kill hundreds of thousands of people in Afghanistan, many of them totally innocent. It is also not our function to serve other nations as law enforcement agencies."

"These are warfighters, the best in the world, and they either want to fight to win or not fight at all," Trump continued. "We are working to finally end America's longest war and bring our troops back home!"