Projects funded by the Asian Infrastructure Investment Bank must not add to the receiving country's debt burden, the lender's president Jin Liqun said on Tuesday.

"We do not simply lend to the countries for their sovereign guarantees," Jin told CNBC's "Street Signs."

"We work actively with the private sector companies in those countries so that our investments would not build up heavy pressure on their debt burden," he added. "It's very important for our members to continually invest in infrastructure and other productive sectors without creating debt burden."

Jin's comments came amid mounting criticisms that the push for massive infrastructure building in developing countries has increased their debt in an unsustainable way. Those criticisms were particularly directed at China's mega program called the Belt and Road Initiative.

The AIIB — a China-led multilateral development bank — also faced similar skepticism given its focus on infrastructure financing, including projects under the BRI.

Making sure recipient countries can pay back their debt is a priority of the Chinese government, said Zou Jiayi, vice minister of China's Ministry of Finance.

"The Chinese government attached a lot of importance to the debt sustainability when we pursued BRI because we are the creditor, we are the stakeholder. Those are our money," she said earlier this month at the annual meetings of the International Monetary Fund and the World Bank in Bali.

Getting the private sector involved is key to making sure any infrastructure development is sustainable, Jin said. That has been AIIB's focus, which has helped to silence skeptics, he added.

"I'm pleased to see that the skepticism is now history," said Jin. "(The) private sector can create jobs for people and private sector companies can help the developing countries move up on the value chain. So, we think it makes a lot of sense for us to work with the private sector."