He expressed this view in response to an accusation of "hypocrisy" from Sinn Fein MLA Phil Flanagan for not seeking the removal of Union flags in the Chanterhill area of Enniskillen. He said Mr. Elliott had called for Irish flags to be removed from the Cornagrade Road at Easter time.
"It appears that Sinn Fein's Martin McGuinness is going to meet and greet Her Majesty The Queen - and why not? I don't know why there is so much hype about the issue. However it will be another point of acceptance by Irish Republicans that Northern Ireland is indeed an integral part of the United Kingdom," said Mr. Elliott.
Mr. Elliott said there is obvious growing recognition from Sinn Fein that Northern Ireland is an integral part of the United Kingdom and not the Republic of Ireland.
Mr Elliott said: "I always ask that the flag of our nation is flown in a respectful manner and of course do not object when the Union Flag is flown in a proper manner, just as I do not object to the Irish Tricolour flown in a respectful manner in the Republic of Ireland as that is the flag of their nation.
"Mr Flanagan makes an issue of the Irish Tricolours being taken down on the Cornagrade Road. Anyone who uses that road will notice that not all of those were removed, but instead I assume there was a decision to leave some up, maybe just as a provocative measure.
"As always I call on those who fly the Union Flag to do so with dignity and respect."
Mr. Flanagan accused UUP MLA Tom Elliott of "hypocrisy" for not seeking the removal of Union flags which have been put up in Enniskillen last week.
He has called on Unionist politicians to work with him to agree a flags policy for Enniskillen.
Mr. Flanagan said: "Immediately prior to Easter this year, we had the annual call from Tom Elliott for Irish flags to be taken down from the Cornagrade Road. These flags were erected and taken down within a very short period of time as was agreed.
"In stark contrast to this custom is the erection of a significant number of Union flags across Enniskillen, with no indication of a timeline when these flags will be removed nor has there been such a call from unionist representatives.
"There is no justification for the erection of these flags, which has taken place a full month before the 12th of July, and many local people are certain that, as with previous years, these flags will remain up right through to the autumn when they become very torn and tattered.
"Many of these flags are in the Chanterhill and Cavanaleck areas, where there are a number of mixed housing developments and public facilities including the MOT test centre and St Fanchea's College.
"I have previously called for the establishment of a taskforce to deal with the issue of contentious flags and emblems in Enniskillen. Such a group would consist of representatives of each political party as well as local business and community leaders.
"To date, Unionist politicians have been consistently silent on the issue of Union flags and I am calling on them to work with me and others to agree a flags policy for the greater Enniskillen area.
"Our town centres should be neutral areas; free from flags, as should public property while anyone wishing to erect flags for any occasion should be mindful of residents and businesses, with a clear and definitive timeframe for flags to be removed."