Islamic State militants launched their biggest offensive yet outside the Kurdish-controlled city of Kirkuk and tried to penetrate the city itself, in a spate of brazen attacks by the extremist group on Kurdish forces across Iraq.

A senior Kurdish commander, Brig. Gen. Sherko Fatih, was among at least six Kurdish forces killed in the surprise attack southwest of Kirkuk, in northern Iraq, which officials said began just after midnight Friday.

As fighting raged outside the city, fighters from Islamic State, also known as ISIS, staged a bold attack within Kirkuk itself. Local officials said militants tried to break in to the Kirkuk Palace Hotel after detonating a car bomb in front of the hotel, a rare incursion into the city center.

Kirkuk governor Najmaldin Karim said Kurdish forces and local police foiled the hotel break-in, killing three militants. The Kurdish force known as Peshmerga "foiled today a break-in operation by ISIS toward oil and gas installations from three directions that aimed at reaching the center of Kirkuk," Mr. Karim said.

After hours of fighting, Peshmerga officials also said they pushed the militants back from the areas where they had advanced southwest of Kirkuk, focusing particularly on cutting their access to roads leading to oil infrastructure.

Still, the strings of attacks on Friday are a fresh setback for the Kurdish forces at the front line of the fight against Islamic State in Iraq. The militants have fought the Peshmerga and other Kurdish forces around Erbil, the capital of the semiautonomous Kurdistan region in the north, and areas further south closer to Baghdad. But attacks around Kirkuk, the oil-rich city under the control of Kurdish forces, are rare.

Also Friday, Islamic State suicide bombers targeted Peshmerga forces in Jalawla, a Kurdish-controlled town in Diyala province, killing seven Peshmerga fighters. Bomb attacks struck Baghdad and, north of it, the city of Samarra. In western Anbar province, an Islamic State stronghold, militants launched fresh attacks on security forces holed out in Fallujah, security officials said.

Officials in Baghdad and Erbil broadly characterized the attacks across the country as signs Islamic State was lashing out, after losing some momentum and ground in Iraq in recent weeks.

In Syria, Kurdish fighters backed by Syrian rebels and months of coalition airstrikes seized back the city center of Kobani, a Kurdish city on the Turkish border, in a highly symbolic victory for both the Kurds and the international coalition against Islamic State.

Iraqi Parliament speaker Salim al-Jabouri said the Islamic State offensive on Friday came as "cover for the repeated defeats suffered by ISIS." Mr. Jabouri called the Kirkuk attacks "a desperate attempt to undermine stability and social peace witness by Kirkuk."

U.S. officials say the U.S.-led bombing campaign against Islamic State has recently begun to wear on the leadership and operational structure of the militant group, which seized chunks of Iraq and Syria last year.

In Iraq, security forces and Shiite militias battling the Sunni extremist group have made progress in some provinces, but Islamic State controls much of Anbar province in the west and has kept control of Mosul, Iraq's second largest city.

In the north, the militants are still lodged in villages some 30 kilometers on the outskirts of Erbil. Islamic State attacked the area southwest of Kirkuk, the same area under attack on Friday, about two months ago but the offensive then was less sweeping, local officials said. In recent weeks, the group has gathered suicide bombers and foreign fighters in the same area, in apparent preparation for the new attack, the officials said.

Early Friday, under the cover of dark and a particularly foggy night, Islamic State launched the Kirkuk attack from three areas south and west of the city, local officials said: Tal al-Ward, al-Khalid, and Maryam Beik. Airstrikes by the international anti-Islamic State coalition began to hit Islamic State vehicles in the area shortly after, the officials said.

Peshmerga sent in reinforcements and were joined by special counter-terrorism forces from the Patriotic Union of Kurdistan--the Iran-allied Kurdish force blacklisted by the U.S.--in southern Kirkuk for counter-attacks, said Wista Rasool, operations commander in southern Kirkuk province.

By Friday afternoon, the Kurdish forces re-seized key villages and roads leading to oil infrastructure in the city, Mr. Rasool said. Another local security official said the Islamic State commander leading Friday's offensive was killed in the counter-attack.

Dozens of residents across Kirkuk fired guns into the air to celebrate the apparent success of the counter-attack by Kurdish forces, eyewitnesses said, showing how ominous a threat the Islamic State advance on their city was.

Ghassan Adnan in Baghdad contributed to this item.

Write to Nour Malas at nour.malas@wsj.com

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