Mr Tillerson's comments came after he met with Pakistan's Foreign Minister Khawaja Muhammad Asif, who is visiting the US as part of efforts to rebuild bilateral ties frayed after President Trump accused Islamabad of sheltering terror groups.
Mr Asif, during the meeting with Mr Tillerson at the Foggy Bottom headquarters of the State Department, defended his country's role in the war against terrorism.
They held a wide-ranging exchange of views on bilateral and regional issues of mutual interest, a statement by Pakistan's embassy said. Today's meeting signalled a gradual resumption of talks between the two countries that was paused by an upset Pakistan after President Trump announced his new South Asia and Afghan policy.
Mr Tillerson after the meeting told reporters that the US was concerned over the future of the government in Pakistan, adding he believed the US has a partner in Pakistan.
The South Asia strategy rolled out by President Trump was in a regional context, and not just about Afghanistan. "This is about the importance of Pakistan, and Pakistan's long-term stability as well. We have concerns about the future of Pakistan's government too... we want their government to be stable. We want it to be peaceful," Mr Tillerson said.
"Many of the issues they're struggling with inside Pakistan are American issues," he said without elaborating.
The statement issued by Pakistan's embassy said the US and Pakistan shared a common desire for peace and stability in Afghanistan and the region at large. Mr Asif told Mr Tillerson that Pakistan is winning its war against terrorism, the embassy said.