Global index provider MSCI Inc said on Tuesday it will make "bigger jumps" in expanding the presence of China's A shares in its benchmark indices after accessing investor feedback on their initial inclusion on Friday.

The firm is contemplating the possibilities for the next step by either increasing the weighting of large-cap stocks that will imminently be included in its indices this week, or by adding more mid and small-cap stocks, according to Henry Fernandez, chief executive officer of MSCI Inc.

"We don't want to do a large number of small inclusions, but a small number of large inclusions. We want to do bigger jumps," Fernandez said at a news conference in Beijing.

"If we were to include both large and mid-cap stocks, half of the companies covered by the MSCI EM index would come from China," the MSCI chief said, noting that it remains highly uncertain whether foreign investors have the ability to analyze and understand such a large number of new companies from China.

A total of 233 Chinese A-share companies will be officially added to the MSCI indices, including the MSCI Emerging Markets Index, on Friday.

Fernandez said future decisions on A-share expansion would depend on feedback from overseas asset managers, the trading flexibility and smoothness under the stock connect program between Hong Kong and the mainland, as well as the continuous reforms of the mainland market.

The firm is also in close communication with both mainland and Hong Kong regulators to ensure renminbi liquidity in the offshore market, which is crucial for smooth trading by foreign investors.

Fernandez said that the Chinese regulator has allowed greater flexibility for market participants to use data at the mainland stock exchanges to create derivative products and to enrich the investment tools for foreign investors, and he said he believed more progress will be made in the near future.

Foreign investors are eyeing further expansion of A shares in the MSCI indices after the initial inclusion was already viewed as an encouraging sign of China's integration into the global market.

"With the importance of MSCI indices as a benchmark for many institutional investors, we see an opportunity for long-term investors to participate in the Chinese equity markets, particularly if further A-shares are added over time," said Suyi Kim, head of Asia business at Canada Pension Plan Investment Board, the manager of the Canadian pension fund.