Leonard, the managing director of digital for The Independent and the London Evening Standard, said: "We have had thousands of downloads. We are enthused about the uptake."
Leonard would not be drawn on the specific amount of downloads since its launch in November last year.
The app is currently without a headline sponsor. Be Broadband was the exclusive sponsor of the app at launch in November for a period, understood to be six weeks.
Leonard said he was taking to a number of commercial partners, including Be Broadband, about sponsorship opportunities.
The new app features include a credit-based payment system that enables customers to download the app at their will, unlike at launch.
Previously, the subscription for 10 issues, priced at £1.79, ran out in 10 days, as did the 20-copy subscription model.
Leonard also said the app has improved capability to embed multimedia, enhancing its appeal to users and advertisers alike.
The i is currently advertising on TV and earlier this month took over sponsorship of the Heart radio breakfast show.
Leonard said both initiatives had driven customers to download the app.