U.S. President Donald Trump's national security adviser Robert O'Brien said on Sunday that the United States would be unlikely to sign a broader agreement with the Taliban should the latter fail to comply with a reduction of violence deal. 

The broader agreement is expected to ultimately bring about a cut in the number of U.S. troops from around 12,000 down to 8,600, and would also address some U.S. top interests

Read more: Is peace in Afghanistan on the horizon? The peace process examined

"If the Taliban does not live up to their agreement on the reduction of violence plan, then we'll take a very careful look at it, and I think it'd be unlikely that we'd sign a peace treaty," O'Brien said during an interview with CBS News.

"We're not going to reduce troops to a level below what is necessary to protect American interests and our partners in Afghanistan," he added.

Earlier in the day, Trump told reporters before starting his trip to India that the Taliban "are tired of fighting," and both the United States and the Taliban seek to make a deal.

The so-called seven-day reduction in violence, which started on Saturday, could be a test for the Taliban leadership to prove its control over its fighters ahead of signing a peace deal with the United States to end the war in Afghanistan.

According to security officials, no major security incidents have been reported from across the country.

Only a convoy of security forces came under attack in Shah Wali Kot district of Kandahar province at 10:30 a.m. local time Sunday, provincial police spokesman, Jamal Barikzai, confirmed.

However, no one has claimed responsibility for the attack that left no casualties.

The United States and the Afghan Taliban said on Friday that they are set to sign an agreement on February 29 after the implementation of a week-long violence reduction in Afghanistan.

Peace talks between the United States and the Taliban began in 2018 and have now hit 11 rounds but the process has been on-and-off due to intensifying violence for which the Taliban are largely responsible. Washington's latest re-engagement with the Taliban only started in December, a month after Trump decided to pump the breaks for a moment because of Taliban attacks on U.S. assets in Afghanistan.

The war in Afghanistan is the longest one in U.S. history. The death toll of U.S. service members has surpassed 2,400 since the country invaded Afghanistan in 2001. Trump has long grumbled about the U.S. military presence in Afghanistan that started in 2001, calling it "ridiculous."