The Electoral Office has been accused of failing to appreciate "how completely inappropriate" the display of Union flags was in a south Belfast polling station.
The interim chief electoral officer told The Irish News last month that she did not regard bunting in the assembly hall of Blythefield Primary School in the Sandy Row area as excessive.
However, SDLP MP Claire Hanna and party colleague Matthew O'Toole have written to Sarah Ling seeking a meeting to discuss the controversy.
Ms Ling is in post until August when she will be replaced by David Marshall, whose appointment by the secretary of state was announced on Monday.
In their letter, the senior SDLP figures say they were contacted by voters who felt the "venue fell far short of the neutral environment expected and was not conducive to voting in an atmosphere free from fear".
SDLP councillor Gary McKeown, who represents Botanic DEA where the polling station is located, told The Irish News it was important that elections are run "with complete impartiality and fairness".
"No one should feel uncomfortable entering a polling station and there should be nothing on display that causes this, whether it's flags, regalia or other emblems," he said.
"As a society we are becoming increasingly diverse, and the Botanic electoral area is a key example of this, so for this incident to happen here is particularly concerning."
Mr McKeown said there was a failure to acknowledge the seriousness of the situation.
"It's also frustrating that the Electoral Office appears to lack appreciation for how completely inappropriate this was, and doesn't seem to have in place robust arrangements to prevent such incidents from happening," he said.
"There's a need to address a number of outstanding issues around the operation of polling stations, and we will be seeking a meeting on this as resolving them will be essential to ensure confidence in future elections."
A statement from the Electoral Office said staff at polling stations are asked to "remove anything in the room to be used for the election that could be deemed offensive prior to the election".
"We do not request our polling station staff to remove flags or religious symbols from the polling premises," the statement said.
"Where there are concerns, the polling station staff can discuss the issue with the office to determine if further action is required."
Meanwhile, the erection of UVF flags close to Windsor Park in south Belfast has been criticised.
It comes days after UDA flags were placed outside the PSNI training college in east Belfast and close to the Tesco store at Newtownbreda.
Northern Ireland are due to play Kazakhstan at Linfield FC's home ground on June 19.
Alliance councillor Emmet McDonough-Brown said: “There is no place for flags or any other insignia from proscribed terrorist organisations on our streets.
“I call on those who erected these flags to remove them immediately and the organisations they represent to disband and leave the stage once and for all.”
The Irish FA has confirmed that the land on which the flags have been erected is not owned by the association and is therefore outside its jurisdiction.
