Hagel, who flew to Baghdad to get a first-hand report on progress against the Islamic State militants, was holding a series of meetings with top Iraqi government officials and conferring with American military commanders.
He met with al-Abadi at the prime minister's office after making remarks to a group of US and Australian soldiers at Baghdad International Airport.
Al-Abadi told Hagel as their meeting began that "Daesh (Islamic State) is on the descent at the moment." He said their capabilities had been reduced.
US officials assert that the Iraqis' biggest need is competent military leadership, not additional military hardware.
The prime minister said the Islamic State had acquired extensive weaponry and remained able to move back and forth between Iraq and Syria. That contrasts with statements by US commanders who say the militants' ability to resupply their fighters in Iraq has been severely constrained by airstrikes.
"Just as in Afghanistan, it is their country," Hagel said. "They have to lead. They are the ones that are going to have to be responsible for end results."
Hagel said the Baghdad government must bring the country together after disastrous years of sectarian division that undermined much of what the US did to train Iraqi security forces.
"The inclusiveness of a government that all their people can join and be part of and have confidence in and trust in is going to be essential to their future," he said.
Hagel said yesterday during a visit to Kuwait that he believes Iraq's security forces have gained a new momentum, thanks in part to sustained US airstrikes against Islamic State militants.
The US is committed to helping Iraq roll back the territorial gains the militants made earlier this year, but President Barack Obama has ruled out sending American ground combat forces. He maintains that any lasting solution in Iraq can only be carried out by a newly unified Iraqi government.
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