The counter-offensives against the militants came as the UN refugee agency said it was launching a major operation this week to help "close to half a million people" who have been displaced.
US President Barack Obama hailed the recapture of the Mosul Dam but warned Baghdad that "the wolf is at the door" and said it must move quickly to build an inclusive government.
The dam was the biggest prize yet clawed back from the Islamic State (IS) jihadist group since it launched a major offensive in northern Iraq in June, sweeping aside Iraqi security forces.
"This operation demonstrates that Iraqi and Kurdish forces are capable of working together and taking the fight to (IS)," said Obama.
"If they continue to do so, they will have the strong support of the United States of America," he promised, in his clearest signal yet that the 10-day-old US air campaign was far from over.
US and other officials have repeatedly stressed that military cooperation between the Kurds and Baghdad was key to any successful counter-offensive, but their alliance remains uneasy.
"We are the ones who liberated the dam, not the peshmerga," said one of several members of the federal special forces who climbed on top of two vehicles to shout at journalists gathered at a Kurdish checkpoint.
- Fresh fighting near dam -
Fighting erupted Tuesday in the area surrounding the dam and US warplanes carried out fresh strikes targeting IS, a senior officer in the Kurdish peshmerga forces told AFP.
As anti-jihadist forces tried to reclaim ground lost earlier this month in the north, the government launched an operation to recapture the city of Tikrit, further south.
"The Iraqi army and (Shiite) volunteers, backed by Iraqi helicopters, are taking part" in the operation to retake the hometown of executed former president Saddam Hussein, a high-ranking army officer told AFP.
But the offensive stalled later Tuesday and security forces pulled back from the city, witnesses, a police officer and an anti-government fighter said.
Tikrit fell on June 11 and has since been controlled mostly by Sunni militant groups, including former members of Saddam's ruling Baath party.
The government, whose forces folded when jihadist-led militants swept across five provinces more than two months ago, has made Tikrit a priority but has already failed twice to retake it.
US military aircraft have carried out 35 air strikes against IS militants in Iraq over three days, destroying more than 90 targets, the Pentagon said.
Obama justified the strikes, the first US military intervention in Iraq since troops withdrew in 2011, with the risk of genocide against the Yazidi minority and a threat to US personnel in the Kurdish capital of Arbil.
- Major UN aid operation -
Two months of violence have brought Iraq to the brink of breakup, and world powers are relieved by the departure of divisive premier Nuri al-Maliki, who stepped down last week, hoping his successor will be a unifying figure.
In the north, members of minority groups including Christians, Yazidis, Shabak and Turkmen, remain under threat of kidnap or death at the hands of the jihadists, while tens of thousands of others have fled, prompting the UN to announce the major aid operation.
"Conditions remain desperate for those without access to suitable shelter, people struggling to find food and water to feed their families, and those without access to primary medical care," said Adrian Edwards, spokesman for the UN refugee agency UNHCR.
And the son of the Yazidi religious group's leader warned Tuesday that the community is facing "genocide" in Iraq and called for international action.
Meanwhile, IS supporters launched their latest social media effort, starting the hashtag "#AmessagefromISIStoUS" to mark posts on site Twitter, threatening the United States with remarks such as: "We will drown all of you in blood."
IS also warned that the US "will soon disappear... at the hands of the knights of the Caliphate."
The jihadists, who declared their "caliphate" over a vast region straddling the Iraq-Syria border, have also came under attack in their Syrian stronghold of Raqa by Syria's air force.