During the meeting, held in Washington on Tuesday, the two discussed the ongoing situation in Ukraine, the escalating crisis in South Sudan and the recent abduction of more than 200 school girls by Islamic militant group Boko Harm in Nigeria.
Both Ashton and Kerry placed the ongoing Ukraine situation at the top of the agenda. The British official told the press conference that the "latest news of the great concern that we have from the illegal actions by armed separatist groups is, of course, at the foremost of our attention".
"We want to see Russia join in in the call to see an immediate end to these actions… in line with the discussions we had in Geneva, where we talked practically for seven hours.
"We talked about what this meant. There was no vagueness. There was absolute clarity in what we were trying to do - to try and find ways to begin the de-escalation.
"We will continue, as the European Union, to engage fully in seeking a political solution and to stay fully behind what we said in Geneva and to find ways that we can see the implementation done by everyone," she explained.
The EU official said that Ukraine has "the right to defend its territorial integrity" and that "we understand the international obligations that it has, and we work closely with them."
"We have been, it is fair to say, nothing less than disappointed to see Russia to fail to live up to the very plain and simple, easy-to-interpret commitments that were made in Geneva"-John Kerry
"We are focused on the elections and the importance of free and fair presidential elections. This is a really important step in the stabilisation of Ukraine," Ashton stressed.
"It’s about democracy, " she continued, "It’s an opportunity, too, for there to be a legitimate and broad debate on the future of Ukraine and to engage with people who do want to talk about how that future should be - peacefully working together, and to take this opportunity to be able to do that.
"We, of course, will continue as well with our assistance package, which, as you know, will bring in overall support of about €11bn."
Her US counterpart echoed many of the same points, and praised Ukraine for showing "remarkable restraint".
"We have been, it is fair to say, nothing less than disappointed to see Russia to fail to live up to the very plain and simple, easy-to-interpret commitments that were made in Geneva.
"The agreement that we made in Geneva, it really isn’t vague and it’s not open to some loose interpretation. It was simple, it was specific, and it outlined concrete steps that all of the parties had to take.
"Ukraine’s government, literally before the ink was dry, started to implement on that agreement. And they have held up their end of the bargain.
He said that the EU and US "are not going to sit idly by while Russian elements fan the flames of instability, instead of fulfilling the commitments that we made".
On South Sudan
Moving on to the issue of South Sudan, Ashton said that she feared that the country "is on the brink of what could be a civil war, ethnically motivated".
She continued, "The prospects of famine and the humanitarian disaster - they’re really looming large now, so we need to work together.
"[South Sudan] is on the brink of what could be a civil war, ethnically motivated"-Catherine Ashton
"We need to work to ensure that the leaders in South Sudan really do take the action that you’ve identified they need to.
"We need to work very closely in good cooperation with [the US] and with others and to make sure that we put as much energy as possible into trying to prevent what, as I said, could be a disaster."
Meanwhile, Kerry was critical that "the cessation of hostilities agreement that was signed in January by the South Sudanese government and the opposition has obviously not been upheld".
"The recent attacks by the South Sudanese government and the anti-government forces, both of them, are absolutely unacceptable
"We will do our utmost to prevent South Sudan from plunging back into the violence and despair that tore that country apart for so long"-John Kerry
"We will do our utmost to prevent South Sudan from plunging back into the violence and despair that tore that country apart for so long.
"We will continue to stand with the people of South Sudan who call for peace and who recognise that the only way to resolve this conflict is through a political dialogue," he finished.
On the Nigerian schoolgirls situation
Finally, the pair moved on to the troubling scenario in Nigeria, where more than 200 schoolgirls have been abducted with, according to Islamic militant group Boko Harem, the intent to be sold.
"Our thoughts are with the parents of the Nigerian girls and with the girls themselves," said Ashton.
"What has happened to [the Nigerian schoolgirls] is devastating for all of us"-Catherine Ashton
"These are the future of the country. They are teachers, dancers, politicians, they are scientists, they are mothers.
"They are women in the making, who have a right to play their full part in their society. And what has happened to them is devastating for all of us, and we must do… everything possible to try and reunite them with their families and to prevent this ever, ever happening again," she urged.
Kerry reiterated her sentiments, saying, "We remain deeply concerned about the welfare of these young girls, and we want to provide whatever assistance is possible in order to help for their safe return to their families," he concluded.