Mr Ahmed sent a lawyer with a letter pleading a week's time on account of ill health. Iqbal Ahmed was the first Trinamool leader to be summoned in the case.
Almost at the same time, Kolkata Police summoned Mathew Samuel, the journalist who released the sting tapes in March last year, to appear before it on 15 June for an extortion case filed months ago.
Mr Samuel was also recently questioned by the Enforcement Directorate.
The Narada sting operation, shot just before the 2014 general polls, and conducted by Mr Samuel, chief executive of the web portal naradanews.com, supposedly shows a dozen top Trinamool leaders and one IPS officer taking wads of cash from him. Mr Samuel pretended to be a businessman seeking favours from the ruling party.
Among the leaders accused of taking money are senior MPs Mukul Roy, Sougata Roy, Sultan Ahmed, Suvendu Adhikari and MLAs Sovan Chatterjee, Madan Mitra, Firhad Hakim and Iqbal Ahmed, among others.
Mr Samuel has said his first contact in the Trinamool was Iqbal Ahmed, who is also the brother of parliamentarian Sultan Ahmed. Iqbal Ahmed led Mr Samuel to all the other leaders who took a total of Rs 80 lakh from him.
Trinamool Congress chief and Chief Minister Mamata Banerjee initially said the sting tapes were fake. But forensic labs have confirmed the tapes are genuine. The matter is now assigned to the CBI for investigation.