Gen. Ashfaq Kayani is to replace Musharraf as army chief by Nov. 15, provided the Supreme Court confirms Musharraf's victory in last weekend's presidential election.
After a visit to Pakistan's militant-troubled northwest, Kayani "reiterated that there would be no let up in the war against terrorism till it is taken to its logical conclusion," a military statement said.
In his first publicized comments on the situation in the troubled Waziristan region, Kayani told commanders there to "spare no effort in eradicating the menace of terrorism," the statement said.
Fierce fighting between troops and pro-Taliban militants in North Waziristan, a remote region next to the Afghan border, has killed some 250 people this week.
The bloodshed has revived accusations from Musharraf's opponents that he is killing fellow Pakistanis and destabilizing the country to placate Washington.
Friday's statement underlined expectations that Kayani, a close associate of Musharraf, would largely sustain Islamabad's close cooperation with the United States.
Earlier this month, he promoted Kayani, a former chief of the powerful Inter-Services Intelligence agency, to full general and made him vice-chief of army staff.
Musharraf has vowed to step down as army chief and restore Pakistan to civilian rule once he secures another five-year presidential term.
He won a landslide in Saturday's ballot of lawmakers which was largely boycotted by opposition parties.
However, the Supreme Court has said the result can only become official once it rules on challenges to his eligibility for elected office.
Musharraf has called for moderates to join forces after parliamentary elections, to be held in January, and stiffen Pakistan's effort against extremism.
U.S. officials have welcomed the intensified military operations in the area near the Afghan border which they say offers a safe haven for al-Qaida leaders and a strategic base for Taliban militants fighting NATO troops in Afghanistan.