Secretary of State Rex Tillerson put Pakistan "on notice" Tuesday that it must stop sheltering terrorists or risk losing its status as an American ally.

"We are going to be engaging with them in a very serious and thorough way as to our expectations and the conditions that go with that," Tillerson told reporters at the State Department.

Those conversations will seek to implement President Trump's new strategy for prosecuting the war in Afghanistan, with an emphasis on cooperation with India and Pakistan, which are traditional enemies. Pakistani officials responded by touting their record opposing jihadists, but the government has long been accused of training militants to fight against India, including an insurgent group that has warred against the United States and Afghanistan's central government.

Tillerson refused to rule out U.S. airstrikes in Pakistan. "We are going to attack terrorists wherever they live," he said. "And we have put people on notice that if you are harboring or providing safe haven to terrorists, be warned, be forewarned."

In 2010, then-President Barack Obama's decision to authorize a Navy SEAL mission to kill Osama bin Laden outraged Pakistan, which regarded the raid as a violation of its sovereignty. But Tillerson suggested that the Trump team will use a broad array of tools as leverage over Pakistan, including sanctions or even the withdrawal of Pakistan's status as a major non-NATO ally.

"All those things... are on the table for discussion, if, in fact, they are unwilling to change their posture or change their approach to how they're dealing with the numerous terrorist organizations that find safe haven in Pakistan," Tillerson said.

It shouldn't need to come to that, he emphasized. "In my view, the greatest [beneficiary], other than the Afghan people themselves, to achieving stability and peace in Afghanistan are the people of Pakistan," Tillerson said. "It is in Pakistan's interest to take those actions."