Rajapaksa's government, already under pressure from the United States and other countries over the proceedings against the scholarly Bandaranayake, also met with opposition from the country's lawyers who have refused to accept a new chief justice.
The Colombo Page reported that besides the lawyers, opposition parties refused to take part in the nomination process.
Bandaranayake, an academic who became Sri Lanka's first woman chief justice after being appointed to the post by the Rajapaksa government in 2011, was dismissed over the weekend after being found guilty of amassing wealth and property and not declaring her assets, charges she had strongly denied.
Last week, a high court, acting on her appeal, ruled a Sri Lankan parliamentary committee had no legal standing to impeach Bandaranayake and any such action can only be taken based on law passed by Parliament.
Following that, the Sri Lankan Parliament, where the Rajapaksa Party enjoys strong support, passed an impeachment motion against the chief justice, which allowed Rajapaksa to ratify it and dismiss her.
Political opponents have said the effort to remove her from her post was the result of an impasse between Bandaranayake and the executive branch over a bill designed to take away some of the powers of the country's provinces. The government has denied that accusation.
On Monday, Rajapaksa met with the Bar Association of Sri Lanka to discuss the appointment of a new chief justice, Colombo Page reported.
The president was quoted as saying he would not allow special groups to take political mileage out of the situation and drag the country back to the time it was "ruled by a leaflet." The report said he also asked the Bar Association not to make the judiciary a playground for groups trying to achieve political objectives. The lawyers' group denied any affiliations with such groups.
Separately, the newspaper said another lawyers' group called the Lawyers Collective refused to accept the appointment of a new chief justice, saying the removal of Bandaranayake was illegal. The group also called for a united fight to safeguard the independence of the judiciary and the rule of law.
The report said Bandaranayake has so far not made any official statement on her dismissal, but her attorney was quoted as saying she will not recognize the legality of her dismissal even though she has agreed to vacate her official residence.
In her daily media briefing Monday, U.S. State Department spokeswoman Victoria Nuland said the proceedings against Bandaranayake were conducted "in defiance of the Supreme Court order."
Noting the impeachment "raises serious questions about the separation of powers in Sri Lanka," Nuland said the United States had repeatedly conveyed to the Sri Lankan government "our concern that there was a lack of due process, and we've also made very clear our view that actions undermining an independent judiciary would impact on Sri Lanka's ability to attract foreign investment."
Nuland said along with the United States, Britain, Canada, the European Union, and the United Nations have all issued statements "expressing strong concerns about this process."
Earlier, Gabriela Knaul, the U.N. special rapporteur on the independence of judges and lawyers, said attacks against judges and lawyers threaten the independence of the Sri Lankan justice system.
The U.N. official said she has received reports that indicate attacks and threats against Sri Lankan judicial members and lawyers have "dramatically increased" in recent months.