The SDLP's Mark H Durkan has said the number of victims who have alleged vote stealing in Foyle are just the "tip of the iceberg".
He was speaking as all the general election candidates in the constituency - except Sinn Fein - called for an investigation.
The party dismissed the claims of fraud in Foyle - where it snatched the seat from the SDLP with a majority of just 169 votes - as "an effort by political opponents to explain away their rejection by the electorate".
Local SDLP MLA Mark H Durkan met with Chief Electoral Officer Virginia McVea yesterday, bringing forward what he said was evidence from the constituency of "vote stealing".
He says he is aware of 20 cases of electoral fraud and wants the Electoral Office, the police and James Brokenshire to act on the issue.
"The Chief Electoral Officer accepted the fact that this was an issue," said Mr Durkan.
"She says it is not widespread. But in my opinion one incident of this nature is significant. I know of 20 at this stage, with more information coming in.
"I believe that there are numerous people out there who have found themselves in similar situations that have not reported it, and I would urge them to do so.
"This is just the tip of the iceberg. I commend the bravery of those who have spoken out already.
"People are still afraid and embarrassed that this has happened to them, but it's from people coming forward and sharing their experience that we will get the full picture, which will hopefully prompt the Electoral Office, the PSNI and the Secretary of State to take action on this."
The Electoral Office said that Foyle had the highest number of 'pink slips' recorded for Northern Ireland in the general election, with 12 cases being recorded in comparison to just four in the 2016 Assembly election.
Pink slip voting is when people who have been prevented from exercising their franchise are offered a tendered ballot paper instead, the so-called pink slip.
It does not count, but may help estimate the scale of any fraud.
It says it is also dealing with two more incidents relating to people turning up and not being able to vote, and three other complaints.
On Monday the Belfast Telegraph highlighted the cases of four people who claim their votes were stolen in the constituency.
Ms McVea said that the Electoral Office follows up on each instance and that a "handful" of cases have been handed over to the PSNI.
"In total there are 12 pink slips for Foyle," she said.
"Mark H Durkan informed me of two other incidents which I'm following up on. The eligible electorate for Foyle is 70,324.
"In terms of meeting with Mark H Durkan and going through what has come into the office so far, I don't have evidence before me of that.
"I've given the figures as they stand - that's what I have to work with, and I liaise with the PSNI with all of those concerns."
All the parties and candidates, apart from Sinn Fein, have called for a full investigation into the allegations.
DUP candidate Gary Middleton said the evidence of electoral fraud was an "affront to democracy".
"It is clear, as each day passes, that there is more and more evidence from individuals on the electoral register who went to vote and couldn't," he said.
Mr Middleton also raised concerns about the surge of proxy votes in nationalist areas in the Foyle constituency this year.
Sinn Fein said that the allegations of voter fraud were merely an excuse for failure.
"There is always an effort by political opponents to explain away their rejection by the electorate," it said in a statement.