Slamming the "1970s mentality" of those behind a poster telling Martin McGuinness to "rot in hell", Mid Ulster MP Francie Molloy has called for its immediate removal.
In a statement, he said: "As tens of thousands of people gathered in Derry to pay tribute to the life of Martin McGuinness, including Unionist leaders, US President Clinton, Irish Taoiseachs (past and present) and representatives of the British government, it is sad to see that a small corner of Loyalists have not moved away from the 1970s mentality that festered in the murder Triangle of East Tyrone and North Armagh.
"I call on the Unionist political representatives in the area to show leadership and call on the PSNI to have this removed without delay.
"Surely it falls within a hate crime.
"Unfortunately this simply reflects badly on Moygashel and even the nearby Linen Green complex that attracts visitors and shoppers from all parts."
Police and DUP councillor Kim Ashton said they are in talks with the community to have the sign taken down.
Sinn Féin MLA Michelle Gildernew said a picture erected in Moygashel stands in stark contrast to the dignity and respect shown for Martin McGuinness yesterday.
The Fermanagh South Tyrone MLA said: "This picture stands in direct contrast to the events yesterday where tens of thousands came from across Ireland and the globe to pay respects to a political leader in a dignified manner.
"No one did more for the peace process than Martin McGuinness.
"His outreach to everyone regardless of race, gender, class, religion or sexuality was an example to us all and he continually worked to build a better society based on respect, tolerance and equality.
"There is a family mourning the loss of their husband, father, grandfather, brother, uncle and indeed many mourning the loss of a friend.
"I condemn this vile behaviour in the strongest way possible. Actions like this cause concerns and problems for society."
This story was changed at 5.34pm, March 24 to add Michelle Gildernew's statement.