Elsewhere, Syrian opposition fighters in Eastern Ghouta opened fire on civilians protesting against opposition infighting.
The Syrian Observatory for Human Rights, a Britain-based war monitor, said on Monday that the Syrian Democratic Forces (SDF) now control about 80 percent of Tabqa.
The YPG-dominated SDF are fighting to drive Daesh from its stronghold of Raqqa, as well as the east of Tabqa.
Tabqa sits on a supply route about 55 kilometres (35 miles) west of Raqqa, and controls Syria's largest dam, which is under Daesh control.
The SDF on Monday said it had pushed Daesh out of the old quarters of Tabqa.
The US-backed militias broke into Tabqa from the south last week and have steadily advanced north, cornering Daesh in three contiguous neighbourhoods on the bank of the Euphrates River.
The SDF will wait to assault Raqqa until it seizes Tabqa, its military officials have previously said, but it had made slow progress since besieging the town in early April.
Erdogan seeks to sway US policy on Syria
Turkish President Recep Tayyip Erdogan is seeking to discuss ways to change US President Donald Trump's Syria policy.
Turkey last week bombed YPG targets in Syria, triggering criticism from its NATO partner.
On Sunday, Erdogan warned more action could be imminent.
"We can come unexpectedly in the night," said Erdogan. "We are not going to tip off the terror groups and the Turkish Armed Forces could come at any moment."
The YPG is the armed wing of the PYD – the Syrian affiliate of the PKK – which has waged a three-decade insurgency against the Turkish state. The PKK is recognised as a terrorist organisation by Turkey, the US, and the EU.
However, the US sees the YPG as a key ally on the ground in the fight against Daesh in Syria, and Trump has continued his predecessor's policy of actively supporting the group.
Turkey says it will take part in the US-backed Raqqa offensive if PKK-linked groups are not involved in the fighting.
Analysts say the dispute over US support for the YPG will be high on the agenda when Erdogan meets Trump on May 16 in the United States.
Clashes ongoing elsewhere
The White Helmets on Monday said a regime rocket attack on a opposition-held town in western Aleppo's countryside killed 16.
The rescue workers said they responded to a blast that levelled a three-storey building in Awejel town overnight which appeared to be from a surface-to-surface missile. Four women and nine children were among the dead while three people were rescued.
Elsewhere, footage has emerged of Syrian opposition fighters firing on civilians who were protesting the deadly infighting within the opposition in Eastern Ghouta, injuring at least 12 people.
The footage – posted by the Ghouta Media Centre activist group – shows protesters running for shelter after coming under fire by armed rebels. At least 12 people were wounded in the incident in Eastern Ghouta which is just outside the capital Damascus.
Fighting between rebel groups in the biggest insurgent stronghold near the Syrian capital entered its second day on Saturday.