According to the spokesman of CBN, Mr Isaac Okorafor, he gave the assurance in a statement on Sunday in Lagos State.
The News Agency of Nigeria (NAN) reports that the apex bank had so far kept to its promise of continuing to supply enough forex to guarantee liquidity in the market.
The statement said the bank was committed to ensuring that authorised dealers got sufficient supply to meet the demands of authentic customers of banks.
It disclosed that the bank had since February offered over one billion dollars to the interbank market.
The bank expressed optimism that stability had been restored to the forex market.
According to the statement, individuals can easily access forex to address personal and business allowances.
NAN reports that a summary of the CBN intervention in the interbank market over the past two months, shows the highest bid rate was N360 per dollars, while the lowest was N315 per dollar.