Sabah al-Numan told the BBC that many IS fighters had been killed.
Government forces entered the city's outskirts for the first time on Tuesday since the city was seized in June 2014.
Wednesday is the 17th day of the anti-IS operation, which involves 50,000 personnel including Kurdish Peshmerga fighters and Sunni Arab tribesmen.
Elite troops seized control of the state TV building in Kukjali on Tuesday hours after launching an assault on the eastern district and later breached the outskirts of the Karama district.
A BBC journalist travelling with them said they were facing stiff resistance.
But Al-Numan, a spokesman for the Counter Terrorism Service (CTS) said: "We broke the front line of the centre of Mosul. We liberated a very important area which is the main gate for Mosul from the east.
"We had a very tough fight with ISIS in this area and we could liberate it very fast and also without any casualties, in front of many dead and executed from ISIS."
Mosul is last major urban stronghold of IS in the country.
The BBC's Joan Soley, with the elite Iraqi forces in Mosul
The men of the special forces appear casual - but make no mistake, they are ready.
Many have scars from Ramadi or Falluja or both. They have lost friends. Some are younger than you might expect for the fighting they have experienced.
Many are also recently married - common practice before deploying for battle - and keen to show pictures of their new brides on their smart phones.
From low-ranked soldiers to top generals, all say this is not going to be easy. The mission could take months.
But liberating Mosul is the fight they have been waiting for.
Army units are also pushing into the south-eastern Judaydat al-Mufti area, according to the military.
The operation is backed by air and ground support from a US-led coalition.
On Monday, Iraqi Prime Minister Haider al-Abadi told the 3,000 to 5,000 militants believed to still be inside Mosul that there was "no escape" and to "either surrender or die".
About 1,000 of the militants are thought to be foreigners. Gen Talib Shaghati al-Kenani said they came from Uzbekistan, Turkey and other countries.
"Those are a group of terrorists who fight Iraqis and usurp their cities," Gen Kenani said.
Many people have fled the area but some civilians have returned to their homes in villages around Mosul, some waving white flags to show they are not fighters.
As Mosul is encircled, UN officials have expressed concern for the safety of the 1.5 million civilians estimated to be living there.
The Office of the High Commissioner for Human Rights said on Tuesday that it had received fresh reports of mass killings and forced relocations carried out by IS.
The UN Assistance Mission for Iraq said 1,792 people were killed in October, 1,120 of whom were civilians.