Wasant Meewong, the Bangkok governor's adviser and spokesman, said MR Sukhambhand has no option but to suspend his activities until the court has made its ruling.
The court can reject the EC's request or order a new city election.
MR Sukhumbhand was ready to accept the court's ruling, whatever it may be, he said.
Mr Wasant said all orders signed by MR Sukhumbhand prior to March 29 were still legally effective.
MR Sukhumbhand has signed an order empowering his deputies to act on his behalf from today. The four deputies, in respective order, are: Phusadee Tamthai, Pol Gen Asawin Kwanmuang, Jumpol Sampaopol and Amorn Kijchawengkul.
MR Sukhumbhand thanked all of those who were present at the press conference for giving him moral support.
He said he respects the law, the court and independent organisations under the constitution and believes he will be given justice.
"Politicians can't be above the law, especially those holding a political post. I would also like to ask all politicians of all levels to keep in mind that they cannot place themselves above the law," he said.
MR Sukhumbhand expressed concerns for Bangkok, which he said is a battlefield with no end of conflict in sight.
He said he would never abandon the people because he was re-elected as governor in the March 3, 2013 gubernatorial election by as many as 1.2 million votes.