Islamic State pressed a separate assault to capture government-held parts of the northeastern city of Hasaka, blowing up a security building and triggering a government appeal for all residents to take up arms. The United Nations said 60,000 people were reported to have fled the attack.
Islamic State's twin attacks which began on Thursday showed the group returning to the offensive in Syria after two weeks of defeats at the hands of Kurdish-led forces, supported by US-led air strikes. Earlier this week the Kurds advanced to within 50 km (30 miles) of Raqqa city, the group's de facto capital.
The Kurdish YPG militia described the attack on Kobani as "a suicide mission" rather than an attempt to capture the town at the Turkish border. It said it fought intermittent gun battles on Friday with Islamic State fighters holed up in three locations.
The United States and its allies staged 28 air strikes targeting Islamic State in Syria and Iraq on Thursday, including 10 near the Syrian border town of Kobani, the US military said.
The strikes near Kobani along the border with Turkey hit eight units of Islamic State fighters as well as several vehicles, fighting positions and staging areas used by the militant group, the Combined Joint Task Force said in a statement on Friday.
Islamic State has a record of conducting large scale killings of civilians in territory it captures in both Iraq and Syria, where it has proclaimed a caliphate to rule over all Muslims according to an ultra-hard-line vision of Islam.
The attack on the predominantly Kurdish town of Kobani and the nearby village of Brakh Bootan marked the biggest single massacre of civilians by Islamic State in Syria since it killed hundreds of members of the Sunni Sheitaat tribe last year, Rami Abdulrahman, who runs the Observatory, said.
Elderly, women and children
He said 146 civilians had been killed. The YPG spokesman said at least 145 had died in the assault launched by a group of Islamic State fighters estimated to number in the dozens.
"The Daesh attack was a suicide mission. Its aim wasn't to take the city but to create terror," spokesman Redur Xelil said, using an Arabic name for the group.
The assault included at least three suicide car bombs. The dead included the elderly, women and children.
The Islamic State fighters were reported to have entered the town disguised as members of the YPG and Syrian rebel groups.
Unlike the Kobani raid, the Islamic State attack on Hasaka appears aimed at wresting control of the government-held parts of city, which is divided into areas run separately by President Bashar al-Assad's government and the YPG.
"I call on every man, every young woman and every young man able to carry weapons to move immediately and join the frontline positions to defend the city," Information Minister Omran al-Zoubi said in an appeal on state television.
At least 20 soldiers and members of militia fighting alongside them were killed in the attack on the security building mounted by two suicide bombers, the Observatory said. Zoubi said part of the building was destroyed and a number of people killed.
While Islamic State had managed to advance slightly in Hasaka on Friday, seizing one army position, fierce army air strikes had hindered the attack, Abdulrahman said.
Islamic State said in a statement its fighters had seized control of a road between Hasaka and an army base to the east.
The Observatory denied an Islamic State claim that its fighters had freed prisoners held at the city's central prison.
The YPG, which controls northern parts of the city, says it does not cooperate with government forces.
In the latest attacks, Islamic State has picked targets with a low risk of air support from the US-led alliance. In Kobani, also known as Ayn al-Arab, aerial bombardment risked civilian casualties in the residential areas targeted in the attack.
In Hasaka, the Islamic State targets were in areas controlled by Assad. The US-led coalition, which has been bombing Islamic State targets in both Syria and Iraq since last year, has ruled out cooperating with Damascus.
Huge displacement in Hasaka
Recent weeks have seen momentum shift repeatedly in the battle against Islamic State. The fighters advanced rapidly last month, seizing cities in Syria and Iraq, before the recent Kurdish advances in Syria.
The UN Office for the Coordination of Humanitarian Affairs said an estimated 50,000 people had been displaced within Hasaka city while 10,000 had left northwards towards Amuda town, close to the Turkish border.
It warned that up to 200,000 people could eventually flee.
State news agency SANA said scores of Islamic State fighters were killed in the army air strikes.
Assad has lost territory since March in areas of northwestern, southern and central Syria to a patchwork of armed groups, including Islamic State, other hard-line Sunni jihadists, and rebels who profess a more inclusive vision for Syria.
The Observatory said at least 34 people had been killed in Deraa province in southern Syria since an insurgent alliance known as the Southern Front launched an operation on Thursday to capture the remaining areas of government control. Those killed included rebel fighters and a media activist, it said.
The head of one of the rebel groups fighting in the south said there had been progress, but it was not fast.
"The battle continues," Bashar al-Zoubi, the head of Yarmouk Army, told Reuters.
Al Qaeda's Syria wing Nusra Front also has a presence in the south. SANA said the army had targeted Nusra Front on Friday, killing a number of fighters and destroying their weapons.
The government has focused on shoring up control over the main cities in the west, including Damascus, with vital military support from the Iranian-backed Lebanese group, Hezbollah.