Islamic State fighters launched simultaneous twin attacks against the Syrian government forces and Kurdish militia, near the capital of their "caliphate".
After losses to the Kurds backed by US-led air strikes, Islamic State sought to retake the initiative with incursions into the Kurdish-held town of Kobani at the Turkish border and government-held areas of Hasaka city in the northeast.
In a separate offensive in the multi-sided Syrian civil war an alliance of rebels in the south of the country also launched an attack with the aim of driving government forces from the city of Deraa.
The attacks by Islamic State follow a rapid advance by Kurdish-led forces deep into the hardline group's territory, to within 50 km (30 miles) of its de facto capital Raqqa, hailed as a success by Washington.
The dual assaults on government forces in Hasaka and Deraa - both provincial capitals - are a test of Assad's resolve to hold out in remote outposts beyond the western area of the country seen as the top priority for his survival.
The United States and European and Arab allies have been bombing Islamic State since last year to try and defeat a group, which a year ago proclaimed a caliphate to rule over all Muslims from territory in Syria and Iraq.
Islamic State advanced rapidly last month, seizing cities in Syria and Iraq. The latest Kurdish advance in Syria has shifted the momentum again but Islamic State fighters have often adopted a tactic of advancing elsewhere when they lose ground.
The group said it had seized al-Nashwa district and neighbouring areas in the southwest of Hasaka, a city divided into zones of government and Kurdish control. Government forces had withdrawn towards the city centre, it said in a statement.
Syrian state TV said Islamic State was expelling residents from their homes in al-Nashwa, executing people and detaining them. Many Islamic State fighters had been killed, it said, including one identified as a Tunisian leader.
The Syrian Observatory for Human Rights, which tracks the war, said Islamic State had seized two districts from government control.
Government-held parts of Hasaka are one of President Bashar al-Assad's last footholds in the northeast region bordering Iraq and Turkey, territory mainly run by Kurds since Syria's conflict erupted in 2011.
The Islamic State attack on Kobani, also known as Ayn al-Arab, began with at least one car bomb in an area near the border crossing with Turkey, Kurdish officials and the Observatory said. Islamic State fighters were battling Kurdish forces in the town itself.
Kobani was the site of one of the biggest battles against Islamic State last year. Kurdish forces known as the YPG, backed by US air strikes, expelled the fighters in January after four months of fighting.
YPG spokesman Redur Xelil said Thursday's attackers entered the town from the west in five cars, deceptively flying the flag of the Western-backed Free Syrian Army movement, which has fought alongside the YPG against Islamic State.
"They opened fire randomly on everyone they found," he said. The Observatory said the attackers also wore YPG uniforms. Pictures posted on social media showed at least one dead man in uniform who was said to be an Islamic State fighter.
A doctor in the town, Welat Omer, said 15 people had been killed and 70 wounded, many of them seriously. Some had lost limbs and some of the wounded had been taken to Turkey.
Around 50 people fled to Kobani's Mursitpinar border gate with Turkey after the attack, seeking to cross, local witnesses said. Syrian state TV said the attackers had entered Kobani from Turkey - a claim denied by the Turkish government.
Islamic State militants also killed at least 20 Kurdish civilians in an attack on a village south of Kobani, the Observatory reported.
A Syrian official, speaking on condition of anonymity because he was not authorised to speak to the media, said Islamic State appeared to be trying to divert the focus of forces fighting it because of the pressure it was now under near Raqqa: "I believe this is why they moved to Hasaka - because they felt great danger from the situation in Raqqa."
The Kurdish militia say they currently have no plan to march on Raqqa city.
The Syrian government has faced increased military pressure since March, losing ground in the northwest, the south and the centre of the country, where Islamic State seized the city of Palmyra from government control last month.
"If the battle takes time, we are prepared. We have begun the preparatory shelling but we cannot assess the situation right now," said Issam al-Rayyes, spokesman for the Southern Front.
Deraa's provincial governor Khaled al-Hanous told state TV the insurgents had launched "a real war with intensified shelling with various weapons or artillery on citizens in the neighbourhoods of the city and on hospitals, schools and infrastructure".
The rebels had not made "one metre of progress", he said.