The north Belfast politician denied glorifying terrorism after addressing a demonstration marking the deaths of two IRA men killed by their own bomb near Castlederg, west Tyrone.
As Stormont returned for business on Monday after the summer recess, Democratic Unionist MLA Tom Buchanan alleged his remarks "rang in the ears" of dissidents.
"Mr Kelly's comments tell those republicans if you believe you have a vision of equality and freedom and if you know the risks you are taking you cannot stand idly by or leave it to others," he told the assembly.
"There are dissident republicans today who believe that they cannot leave it to the others of Sinn Féin to deliver their goals and who are prepared to use the very same tactics of Harvey and McGlynn [Provisional IRA bombers killed near Castlederg] in an attempt to achieve that aim.
"That is something that was being promoted by Mr Kelly while he was in Castlederg, stirring up young nationalists to get them to do exactly this very thing, promoting this within Castlederg," the West Tyrone DUP MLA said.
That is why the remarks of Mr Kelly are so dangerous and why this assembly must take a united stand against them.
Tom Buchanan, DUP
The annual event in the county was organised by the Tyrone Volunteers Commemoration - this year coincided with the 40th anniversary of the deaths of two local IRA men Seamus Harvey and Gerard McGlynn.
They died just over the border in Co Donegal when the car bomb they were transporting to Castlederg detonated early.
Mr Kelly was a keynote speaker at the event, which his party supported.
He said on their anniversary: "They were ordinary young men in the extraordinary circumstances of the early 1970s who rose to the challenge of the time.
"They had a vision of equality and freedom and they knew the risks they were taking to achieve it but they could not stand idly by or leave it to others.
"It is a harsh reality of resistance that we lose some of our best activists during armed conflict and Seamus and Gerard along with their other comrades whom we remember here today, paid with their lives."
Several hundred bandsmen and republican supporters took part in the march which commemorated republicans from the area who died during the Troubles. Hundreds of protesters, including some family members of IRA murder victims, staged a counter-demonstration on the day amid emotional scenes.
Mr Kelly has argued that he was honouring comrades who gave their lives in the struggle for Irish freedom. He said the centre of Castlederg was supposed to be a "shared space" and almost 20 unionist marches had taken place in the town so far this year.
The senior republican also said there must not be "a hierarchy of victims which would discriminate against republicans and nationalists not just in life, but in death also".
If you are going to criticise someone, it is best to know what they said before you do so.
Gerry Kelly, Sinn Féin
On Monday, Mr Kelly read large extracts of his speech to MLAs.
"As there is so much interest in it, which took me by surprise more than most, I will put a copy of it in the Library so that people might read it," he told them.
"I spoke to a number of unionists and loyalists about this speech and all except one had not read it.
"I doubt very much that Members who are going to speak about it today have even read the speech. That is why I quoted it today."
The DUP motion criticising his comments at the Castlederg IRA commemoration was carried by 52 to 24.
Meanwhile Northern Ireland Secretary Theresa Villiers told the Northern Ireland Grand Committee of MPs, sitting at Stormont, that she was greatly concerned by the Castlederg parade.
"A key way forward for Northern Ireland is for people to take into account the the views of other parts of the community and trying to ensure these decisions are taken in an atmosphere of respect and understanding," she said.
"I hope we will receive a different outcome next year."
DUP MP Ian Paisley Jnr said community relations in Co Tyrone were at an all-time low because of the "diabolical" parade.
He said that the Northern Ireland Secretary "must put a marker down that next year this parade will not be allowed, this error will not be repeated next year."
Ms Villiers said that this summer she was unable to intervene unless asked to do so by the PSNI chief constable.