Shortages of imported food, fuel and medicines have brought thousands onto the streets in over a month of mostly peaceful protests. Rajapaksa declared a second state emergency in five weeks on Friday.
The multilateral AIIB, founded in 2014 to promote infrastructure investing throughout Asia, draws most of its funding from China.
China is Sri Lanka's largest bilateral lender, with an outstanding balance of $6.5 billion mostly lent over the past decade for large infrastructure projects, including highways, a port, an airport and a coal power plant
Beijing has extended Sri Lanka a $1.3 billion syndicated loan and a $1.5 billion yuan-denominated swap to boost its reserves. The two countries are in talks for a $1.5 billion credit line and a fresh syndicated loan of up to $1 billion.
Colombo said this month that talks had started on refinancing Chinese debt after Sri Lanka suspended some of external debt repayments in April.