The US-led coalition that launched operations against IS two years ago is providing crucial backing to both offensives
Capturing Bashiqa was one of the final steps in securing the eastern approaches to Mosul, three weeks into an offensive by Iraqi forces to retake the country's second city.
The town was now under the "complete control" of Kurdish peshmerga forces, Jabbar Yawar, the secretary general of the Kurdish regional ministry responsible for the fighters, told AFP.
"Our forces are clearing mines and sweeping the city," Yawar said.
Iraqi forces have been tightening the noose around Mosul since launching the offensive on October 17, with elite troops last week breaching city limits.
Upping pressure on the jihadists, the Kurdish-Arab Syrian Democratic Forces (SDF) alliance on Saturday launched its own offensive on IS's other main bastion, the Syrian city of Raqa.
Raqa and Mosul are the last major cities in Syria and Iraq under the jihadists' control and their capture would deal a knockout blow to the self-styled "caliphate" IS declared in mid-2014.
The US-led coalition that launched operations against IS two years ago is providing crucial backing to both offensives, with air strikes and special forces advisers on the ground.
SDF forces have been pushing south from areas near the Turkish border towards Raqa and alliance spokeswoman Jihan Sheikh Ahmed said Tuesday they had moved to within 36 kilometres (22 miles) of the city.
"Two more villages have been taken since yesterday," she told AFP, adding that SDF forces had so far advanced 14 kilometres (nine miles) closer to Raqa from Ain Issa, the main staging point for the operation.
"The fighting continues; morale is good and our fighters are determined that this offensive will succeed," she said.
SDF commanders said IS has been fighting back with its favourite tactic of sending suicide bombers in explosives-packed vehicles against advancing forces.
Many of the attacks have been foiled by coalition air strikes or anti-tank fire, they said. SDF forces have been seen digging trenches and piling sandbags in retaken areas to reinforce their positions.
Like in the battle for Mosul, the goal of the Raqa offensive is to surround and isolate the jihadists inside the city, before eventually mounting a street-to-street assault.
In both cases officials are warning of long and bloody battles ahead, as jihadist forces are expected to put up a fierce fight and use trapped civilians as human shields.
More than a million people are believed to be in Mosul. Raqa had a population of some 240,000 before the start of the Syrian civil war in 2011 and more than 80,000 people have since fled there from other parts of the country.
Driving IS from both cities has been the endgame since the US-led coalition launched air strikes against it in 2014, shortly after the jihadists seized swathes of Syria and Iraq.
Iraqi forces scored another victory against IS on Monday by establishing full control over Hamam al-Alil, about 15 kilometres (nine miles) from the edge of Mosul and the last town of note on the way to the city from the south.
Iraqi forces said they found a mass grave at an agricultural college in the Hamam al-Alil area, with the offensive's Joint Operations Command saying "100 bodies of citizens with their heads cut off" had been uncovered.
An AFP journalist at the scene saw body parts and bones mixed with trash at the grave site in the desert west of the town.
But it was not possible to determine the exact number of victims.
Iraqi fighters pulled two bodies, one of which was headless, out of the grave using ropes, the journalist said.
IS's rule has been marked by atrocities including mass beheadings and other executions that it has documented in photos and videos that its supporters share online.
Iraqi fighters are advancing on Mosul from the north, east and south.
The eastern front has seen the most progress, with special forces battling IS inside the city.
Iraqi forces have also moved close to the city from the north but those on the southern front, who had the farthest to go, have still not reached the city's outskirts.
Unlike in Iraq where the coalition has a state-controlled ally in federal forces, in Syria its ground partner is comprised of local militias, including some rebel groups that have battled President Bashar al-Assad's regime.
The domination of the SDF by the Kurdish People's Protection Units (YPG) has also raised deep concerns in Turkey, which considers the YPG a "terrorist" group linked to the outlawed Kurdistan Workers' Party (PKK).