Haider al-Abadi said airstrikes, weapons deliveries and training by the international community had helped roll back the group. As he boarded a flight to Washington, he told reporters more help was needed.
"We can finish Daesh [an Arabic acronym for ISIS] ...and we can stop their advance in other countries," he said, according to the Associated Press.
"We are the only country with armed forces on the ground fighting Daesh. We need all the support of the world."
The visit comes amid differences between Baghdad and Washington over strategy following the group's ouster from Tikrit, and particularly over the role of the Shia Popular Mobilisation militia, which has been accused of abuses against Sunni residents following the battle for Tikrit.
"Abadi is trying to get American agreement for the Popular Mobilisation to take part in the battles for Anbar and Mosul," a source in the National Coalition, a parliamentary group led by Ammar al-Hakim, told Al-Araby Al-Jadeed.
"Washington has flatly refused to any participation by coalition air forces in battles that the Popular Mobilisation militia is taking part in, including the battle in Anbar."
Last month Human Rights Watch accused Iraqi militias of engaging in "deliberate destruction of civilian property" after forcing Islamic State to retreat from the town of Amerli, in Salaheddin province, in early September 2014.
Last week, Iraqi defence sources said the militia would not take part in the battle for Mosul.
Over the weekend, Iraq's Minister of Foreign Affairs Ibrahim al-Jaafari denied that the Popular Mobilization militias have committed sectarian crimes against Sunnis. He said the Iraqi army is in full control of the fighting in Iraq, and denied that there are Iranian forces fighting alongside Iraqi government forces.
On Sunday, Jaafari personally invited an Al-Araby Al-Jadeed correspondent to visit the front lines with him in order to see "the falseness of claims that Popular Mobilization forces burned houses and shops belonging to residents of Tikrit after entering the city with the Iraqi army last week."
Jaafari said the fight against IS requires coordination between countries. In the war, he said, Iran is only playing an advisory role similar to the US. He added that Commander of the Quds Force of the Iranian revolutionary Guards Qasim Soleimani is an adviser, not a combatant in Iraq, and that he did not know the number of Iranian advisors in Iraq.
"Abadi will reassure [the Americans] that this militia's aggressive behaviour against Iraqi Sunnis will be brought under control," said a source close to the delegation in Washington.
Battle for Anbar
Abadi's visit comes as the battle intensifies for Ramadi and Fallujah in the western, largely Sunni province of Anbar. On Sunday night Iraqi air strikes hit the city of Karma, north-east of Fallujah, killing 14 people from three families, a doctor in the city's hospital told Al-Araby Al-Jadeed.
The head of Anbar's provincial council, Faleh al-Issawi, warned that IS fighters were within half a kilometre of the army's command centre in the province. He told reporters that the Popular Mobilisation militia had withdrawn from the Sijariya area east of Ramadi at the start of the battle, saying their withdrawal had made it easier for Islamic State to enter the area.
"The Popular Mobilisation has lost the trust of everybody, even the tribes who had supported its entry into the province," he told reporters.
On Sunday, a series of bombings targeted public places in the capital, Baghdad, killing 12 people. Police officials said a bomb exploded on a commercial street in the city centre, killing four people and wounding nine others.
Earlier, two bomb blasts near an outdoor market killed five people and wounded 10 others in the western suburbs of the capital. Another bomb exploded on a commercial street in Baghdad's district of Amil, killing three people and wounding 11 others.
A video released by IS on Saturday shows militants hammering, bulldozing blowing up parts of the ancient Iraqi Assyrian city of Nimrud, destroying a site dating back to the 13th century BC.
"God has honored us in the Islamic State to remove all of these idols and statutes worshipped instead of Allah in the past days," one militant says in the video. Another militant vows that "whenever we seize a piece of land, we will remove signs of idolatry and spread monotheism".
The destruction at Nimrud, located near the militant-held city of Mosul, came amid other attacks on antiquity carried out by the group now holding a third of Iraq and neighboring Syria in its self-declared caliphate. The attacks have horrified archaeologists and U.N. Secretary-General Ban Ki-moon, who last month called the destruction at Nimrud "a war crime."