Addressing the gathered media at the party's Connolly House office on Saturday, Mr Adams said: "I condemn without reservation the attack on my home and on the home of Bobby Storey.
"I am very thankful that no one was hurt.
"Two of our grandchildren were in the driveway of my home ten minutes before the attack."
"I want to appeal to everyone to be calm. We are involved in a process of change and some people are resistant to change."
The former party leader said if those involved in the attack "have the gumption to sneak up on our homes" then "they or their representatives should come and meet me".
"I would like them to have the guts and the gumption to sit down and tell what this is about," he said.
"I would also like those who are involved in exploiting children in Derry or those who are poisoning the atmosphere in east Belfast to do the same.
"We are very open and Sinn Fein can be contacted through any of our offices.
"That's my direct appeal to them.
"Come and sit down and explain to me what this about, give me the rationale for this action."
A number of prominent political voices have hit out at the attack.
In a tweet, Taoiseach Leo Varadkar wrote: "I unequivocally condemn the violence in Derry and Belfast last night. We will not allow a small minority intent on violence to drag Northern Ireland back to the past. We stand with the decent law-abiding people from all communities in the North."
Alliance Party leader Naomi Long tweeted: "It seems this week some people are determined to drag us back into violence at whatever cost. We need to stand together against all violence. No exceptions. No excuses."
Anyone with any information about the incidents is asked to contact police at Musgrave on 101, with the reference number 1691 and the date 13/07/18.
The public can also contact independent charity Crimestoppers independently on 0800 555 111.