Saoradh is the political wing of the New IRA.
The terrorist group carried out the murder of journalist Lyra McKee who was shot dead last Thursday in Derry.
Paddy Gallagher, spokesman for Saoradh, said that the party was aware the accounts have been suspended.
He added that there would be “no comment”.
In a statement, a Twitter spokesperson said: “We have clear Terms of Service in place which we enforce when violations are identified.”
According to its terms of service, common reasons for suspending a Twitter account include spam, account security at risk and abusive tweets or behaviour.
A protest by friends of Ms McKee took place on Monday outside the office of Saoradh in Derry.
A number of women smeared red paint in handprints on republican slogans outside the office.
Police were present but no arrests were made.