State Department spokesman John Kirby said Kerry would use the meetings to "underscore our strong support for the Iraqi government as it addresses significant security, economic, and political challenges".
He added that the secretary of state, on his first visit to Iraq since 2014, would discuss US-led support for Baghdad's efforts to battle the Islamic State jihadist group.
The coalition is carrying out air strikes against IS, and is also providing training and arms to Iraqi forces.
"This is obviously a very critical time here in Iraq and (we) have been working on a lot of different issues in the last year," Kerry told reporters after meeting Jaafari.
Iraq is battling IS, which overran swathes of territory north and west of Baghdad in 2014, while it grapples with a financial crisis caused by plummeting world prices for oil, on which it relies for the vast majority of its revenues.
And Abadi is seeking to replace the current cabinet with a government of technocrats, a move that has faced opposition from powerful parties and politicians that rely on control of ministries for patronage and funds.
Abadi has announced a series of reform measures aimed at curbing government waste and corruption, and improving abysmal public services, but has faced significant opposition behind the scenes, and little in the way of real, lasting change has been accomplished.
In February, the premier called for "fundamental" change and a cabinet including technocrats and academics, as opposed to the current lineup of party-affiliated ministers.
Shiite cleric Moqtada al-Sadr, who led an insurgency against US-led troops, organised a sit-in in the heart of Baghdad to keep up the pressure for reform, and Abadi presented the names of proposed candidates to parliament last week.
But some of Abadi's nominees have faced significant pressure to withdraw, and at least one has already done so.
- Concern over 'political wrangling' -
"In terms of the political wrangling in Iraq, it's certainly an issue that concerns us," a State Department official said.
Kerry will "encourage the Iraqis, while they're dealing with the cabinet reshuffle, not to lose sight of the need to stay focused on the fight against (IS)," the official said.
Jaafari made reference after meeting Kerry to "recent developments in the political process".
Iraqi forces have regained significant ground north and west of Baghdad, including Anbar provincial capital Ramadi and Salaheddin capital Tikrit.
Baghdad's forces are now fighting to retake Heet from the jihadists, and have already regained control of some parts of the town.
Apart from the city of Fallujah, Heet was one of the largest population centres in Anbar still held by IS, and losing it would be the latest in a string of setbacks for the jihadists.
But while IS is losing territory, it is still able to carry out frequent bombings in government-held areas against both civilians and security forces.
And it controls much of Nineveh province in northern Iraq, parts of Anbar to the west of Baghdad, and swathes of territory in neighbouring Syria.
US President Barack Obama said earlier this week that destroying the jihadist group remains his "top priority."
Kerry travelled to Iraq after visiting the small but strategic Gulf kingdom of Bahrain, where he held talks with Gulf Arab foreign ministers on the conflicts in Iraq, Syria and Yemen.
Kerry called on Iran to help end the wars raging in Yemen and Syria, where Tehran and its Gulf Arab rivals are backing opposing sides.
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