ISLAMABAD -- The Taliban have assailed President Donald Trump's rejection of peace talks, interpreting his assertion that "there's no talking to the Taliban" as a dictate to the Afghan government.

An English-language statement released Tuesday said: "The true authority of war and peace is not with the Kabul regime, but with the American invaders."

Mr. Trump on Monday railed against "atrocities" in Afghanistan, ruling out talks with the Taliban after earlier indicating negotiations could be a way out of America's longest war.

"I don't think we are prepared to talk right now," Mr. Trump said Monday at a luncheon organized by the United Nations Security Council, saying the group was "killing innocent people left and right… so we don't want to talk with the Taliban. There may be a time but it may be a long time."

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While officially saying talks remained an option to peace, the Taliban warned that Mr. Trump's rhetoric would most certainly result in more war and bloodshed.

The Taliban took responsibility for a brutal bombing last week that used an ambulance packed with explosives to evade detection, killing more than 100 people in Kabul.

The bombing was the deadliest insurgent attack in Afghanistan so far this year, but it comes amid a dramatic increase in attacks on Kabul, proving the Taliban's ability to strike in the seat of Afghan power more than 15 years after the U.S. invaded to wrest power from the Islamic extremist group.

The attack came just a week after Taliban militants killed 22 at an international hotel in Kabul frequented by Western travelers.

The ambulance attacker used the vehicle to get through a security checkpoint, telling police he was taking a patient to a nearby hospital, said Nasrat Rahimi, deputy spokesperson for the Interior Ministry. The attacker then detonated his explosives at a second check point.

In spite of the continuing attacks targeting Afghan civilians, the Taliban continues to paint itself as an organization aimed at helping regular Afghans -- as long as they live under the group's rule and adhere to its strict interpretation of Islam.

A senior Taliban official told CBS News' Sami Yousafzai that, in a conference call with senior members of the group last week, Taliban leader Mullah Haibatullah Akhundzada insisted that there were no peace talks taking place, and that under his leadership, "we won't sell out the blood of our leaders and soldiers" to engage in any.

Yousafzai's source said Haibatullah used his address to followers to announce new appointments in Taliban leadership, and as a pep-talk ahead of the new year's fighting season.

He said that military strategy of the group "should not only focus on fighting," but also on "helping and making the lives of those living in Taliban (controlled) areas easier."

"We are committed to the restoration of an Islamic regime and we won't compromise on our values," Haibatullah said, according to the source who was on the conference call. "We should be thankful to the almighty that while after 9/11 we had not a single place to hide for a while in Afghanistan, now with the grace of God we have territorial control in Afghanistan."

The Taliban has clawed back significant territory in Afghanistan in recent years, drawing more U.S. troops back into the country to help train and bolster Afghanistan's own beleaguered defense forces.