Former Sinn Féin president Gerry Adams has called on those who attacked his home to meet him.
Mr Adams asked those responsible to have the "gumption and guts" to meet him and explain their actions.
Sinn Féin activist Bobby Storey's house was also attacked and police say the devices thrown at both homes were believed to be "large industrial or commercial fireworks".
Such devices have the capacity to cause serious injury and damage to property.
The attacks took place in west Belfast on Friday night.
Speaking on Saturday, Mr Adams said two of his grandchildren had been in the driveway before the attack but no-one was injured.
Mr Adams said he was unsure whether there was a connection between the attacks and the recent violence in Londonderry, which is being linked to dissident republicans.
In a direct appeal to those who attacked his home, he said: "I'd like them to sit down and explain to me what this is about.
"I'd like those who are involved in exploiting children in Derry to do the same thing, or those who are poisoning the atmosphere in east Belfast and causing havoc to do the same thing."
He said those responsible were "resistant to change" and the groups that had stepped away from the peace process saw Sinn Féin as the enemy.
The Police Service of Northern Ireland said officers were investigating incidents at two houses in west Belfast, after reports were received of loud bangs at both locations at 22:50 BST on Friday 13 July.
"There were no reports of any injuries. However, a parked car was damaged at one of the houses," a spokesman said.
By Chris Page, Ireland correspondent
Gerry Adams has spoken several times in the past about death threats made against him - by loyalists and by dissident republicans who are opposed to the peace process.
Sinn Féin's statement about the attacks on the homes of Mr Adams and Bobby Storey doesn't explicitly pin the blame on republican splinter groups.
However, the party's reference to "increasingly desperate and irrelevant groups" firmly points in that direction - and republicans who have expressed support for Mr Adams on social media have condemned dissidents as "criminals" and "thugs".
A number of hours earlier, Mr Adams's successor as Sinn Fein President - Mary Lou McDonald - strongly denounced the dissidents who are believed to be behind recent rioting in Londonderry as "warped, negative, regressive, dangerous people".
The other attack occurred at the home of Bobby Storey, a senior Sinn Féin figure and a former member of the Provisional IRA.
He was involved in the Maze Prison escape in 1983, where 38 IRA prisoners escaped from the maximum security prison.
The attacks in Belfast came after six nights of violence in Derry, which have taken place around the Twelfth of July parades, which often bring a heightening of tensions centred around the anniversary of the Battle of the Boyne.
Who is Gerry Adams?
Mr Adams, 69, spent nearly 34 years at the helm of Irish republican party Sinn Féin.
During The Troubles Mr Adams survived several attempts on his life, including a 1984 gun attack by loyalist paramilitaries.
He is one of the most recognisable and controversial figures in Irish politics
Two months after the death of Martin McGuinness in 2017, Mr Adams announced he would step down as leader. He was succeeded by Mary Lou McDonald.