The operation comes as US and Russian envoys met in Switzerland to discuss possible routes to a new ceasefire.
Diplomats said the meeting was courteous and businesslike but there would be no statement after the talks.
Since a brief truce collapsed last month, Syrian government forces backed by Russian air strikes have intensified their bombardment of rebel-held areas in Aleppo.
Aid agencies say a 72-hour ceasefire is urgently needed to allow supplies in and civilians out of devastated areas in the east of the city.
Apocalyptic prophecy
Turkish President Tayyip Erdogan confirmed fighters were moving on Dabiq, which lies about 10km (6 miles) from the Turkish border.
Rebel fighters backed by Turkish airstrikes have been edging closer to the town for days, seizing villages around it and all but isolating it.
A bombardment was taking place as part of the offensive on Saturday, a monitoring group and a rebel commander said.
Dabiq is important to IS because it is named in Islamic apocalyptic prophecies as the site of an end-of-times showdown between Muslims and their enemies. The militant group named its magazine after the town.
The advance on Dabiq is part of a wider offensive launched by an alliance of Syrian rebel groups, supported by Turkish forces, in late August.
They are trying to drive IS militants and Syrian Kurdish fighters from an area along Turkey`s border with Syria. Since it began, they have captured the key towns of Jarablus and al-Rai.
`Difficult process`
Meanwhile, US Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov met delegates from Turkey, Saudi Arabia, Iran and Qatar in Lausanne to discuss ways to broker a new ceasefire.
But prospects for success looked bleak. On Friday, Mr Lavrov said he had no "special expectations" for the talks, while a US State Department official told Reuters he did not anticipate a major announcement.
"This is going to be, as it has been now for several years, a very difficult process," the agency quoted the US official as saying.
Syria`s President Bashar al-Assad has vowed to "keep cleaning" Aleppo of rebels and told a Russian newspaper that winning in the city would be a "springboard" to winning in the rest of the country.
Ahead of the talks, organisations including Save the Children, Oxfam, the Norwegian Refugee Council and the International Rescue Committee issued a plea "to establish a ceasefire of at least 72 hours in east Aleppo" to allow evacuations and delivery of aid.
There are now no safe areas left in rebel-held parts of the city, according to REACH, an organisation that contacts people there regularly in order to gather humanitarian reports.
About 275,000 people live in the besieged areas, and aid organisations have not been able to get to them since the siege resumed on 4 September.
More than 370 people, including nearly 70 children, have been killed in the bombardment of eastern Aleppo, according to the UK-based Syrian Observatory for Human Rights.
The monitor said dozens of civilians including children have also died in rebel bombardment of western Aleppo, which is controlled by the Syrian government.
A war that started with an uprising against President al-Assad has now split Syria into many parts. It has been going on for over five years and it has claimed 300,000 lives.
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