Obama said the allies were "making serious progress" in pushing back the jihadists, taking back a quarter of the territory lost last year.
"Success won't occur overnight" Obama said, "but what is clear is that we will be successful."
Critics say Obama's drawdown of US troops in Iraq was a strategic blunder that allowed the Islamic State to flourish and drive Iraq's US-trained army out of northern cities.
Embarking on his inaugural prime ministerial trip to Washington, Abadi had said his top priority would be to secure a "marked increase" in the US-led air campaign and in the "delivery of arms."
Obama did not give that commitment in public, but said the meeting had dealt extensively with coordinating the next steps and possible US help.
Obama said the United States wants to make sure Iraq and the coalition "is in a position to succeed in our common mission."
The US president also announced an additional $200 million in humanitarian aid for the civilians displaced or harmed by the Islamic State's brutal rebel army.
Swathes of Iraq, including the second city Mosul and the vast western province of Anbar, are still occupied by militants bent on establishing an Islamic caliphate.
Abadi renewed a pledged to "liberate" those areas.
But his armed forces, ravaged by years of war, desertion and underfunding, have struggled to get on the front foot.
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A recent Iraqi effort to wrest control of Tikrit stalled until the US military pounded IS positions with air strikes.
Tikrit had initially been seen as a dress rehearsal for Abadi's much-touted "Spring offensive" to dislodge insurgent fighters from the vital oil hub of Mosul.
To defend Baghdad and other key positions Abadi's government has leaned heavily on US-led airstrikes and Shiite militia, which Washington says are controlled by Iran.
Obama called for those fighters to fall under government control, urging all actors to "respect Iraq's sovereignty."
"We expect Iran to have an important relationship with Iraq as a close neighbor," he said, adding: "It is important for all unified forces to be under control."
Abadi said he welcomed help in fighting the Islamic State, but would "reject any transgression of Iraqi sovereignty."
The presence of Shiite militia in Sunni-dominated towns and villages has also raised the specter of more of the sectarian violence that has long plagued Iraq.
Abadi promised his government would have "zero tolerance" of rights abuses, and anyone involved in atrocities against civilians would be brought to book.
Obama has made degrading and destroying the Islamic State a priority, fearing the organization's foothold in Iraq and Syria provides a base for terror operations, while destabilizing those countries and the region.
The United States is leading an international coalition, which according to the White House has hit over 5,780 Islamic State targets in Iraq and Syria.
That includes 75 tanks and 285 Humvees, 1,166 fighting positions, and 151 oil infrastructure-related targets, the White House said.