"You're here because you believe in America. And America believes in you," the vice president told his cheering audience in uniform.
Cheney, a former secretary of defense, took time out from courting Middle Eastern leaders to build support for a wider war to meet with those participating in it.
After arriving by helicopter, Cheney watched both takeoffs and landings from the flight deck. The planes - F-18s and F-14s - were all engaged in active bombing runs in Operation Anaconda.
The fighters left laden with bombs and heat-seeking missiles and would return later in the day without them, Cheney was told.
The vice president ate lunch with the sailors and addressed them all in the cavernous hangar deck.
"This war will end when we and our allies have delivered justice in full measure and no terrorist group or government can threaten the peace of the world," Cheney said.
Earlier, Cheney visited U.S. troops stationed on Oman's Masirah island. Oman has never confirmed the existence of troops there, and Cheney aides would not publicly confirm his destination.
However, officials speaking on the condition of anonymity said Cheney had visited the troops before coming to the carrier. Masirah Island was also listed as a destination in a briefing book on his trip.
Capt. Jim McDonnell, commanding officer of the Stennis, said in an interview that 86 sorties - flights - were scheduled for Friday. Some 5,186 personnel were on the carrier, and most of them jammed into the hangar deck to hear Cheney's speech.
"These forces are just so psyched," McDonnell said.
He said Operation Anaconda against terrorist holdouts in the mountains of eastern Afghanistan was continuing "because we haven't cut the head off yet."
Friday's targets were 700 miles away, McDonnell said.
Cheney praised other members of the international coalition for joining in the battle. As he watched the takeoffs and landings on the carrier deck, a destroyer bearing the flag of Bahrain - a coalition partner - steamed alongside.
Flying on a wall of the hangar where Cheney spoke was a large tattered American flag rescued from the rubble of the World Trade Center towers.
Cheney began his appearance by swearing in a group of those who re-enlisted. "Anybody else out there want to sign up for another term?" the vice president asked.
"I'm in the Middle East on a diplomatic mission, but this is the highlight of my trip," Cheney said. He told the sailors and Marines that he was bringing each of them "the best wishes of the president."
Cheney donned a large white protective floatation vest, a helmet and goggles. The helmet and the vest were both stenciled "VP" on the back.
As he toured the inside of the carrier, Cheney was wearing a pink dress shirt and a blue blazer.
On Thursday Cheney visited the Yemeni capital of San'a under tight security, meeting with Yemeni President Ali Abdullah Saleh.
The leaders both told reporters that they talked about the Israel-Palestinian crisis, Yemen's role in the war against terrorism, and Iraq.
Cheney found little support for U.S. plans for a tougher stance on Iraq, U.S. and Yemeni aides said.
"We have increasingly developed in more recent months very close bilateral relations between the United States and Yemen," Cheney said.
The administration is courting Yemen in hopes of preventing the mountainous, partially lawless country from becoming another Afghanistan by providing sanctuary to fleeing al-Qaida terrorists.
The administration is offering more military training and economic support, but hasn't specified how much. Yemeni officials said they anticipate up to 100 U.S. military advisers within the next few months.
By Tom Raum