CAFOD's message follows the British man killed at the DusitD2 hotel complex on Tuesday in Nairobi being named as Luke Potter.
Militants set off explosions in the luxury hotel's car park before they fired shots and stormed the hotel complex.
Islamic militant group al-Shabab has claimed responsibility for the attack.
CAFOD's Country Representative, Catherine Ogolla described the attacks as "horrifying and worrying", but said communities must not become divided and instead must work for peace and social cohesion.
She explained: "What terrorists of any type want is to divide communities and sow violence, so all peoples must stand together for peace and unity in this time of trouble, sending the message out that any form of violent terror will not succeed; will not divide the Kenyan nation."
Kenya's president has confirmed all the armed terrorists involved in the attack have been "eliminated".
In a televised address, Mr Kenyatta did not say how many attackers were involved but said more than 700 people were evacuated during the security operation.
He also urged Kenyans to "go back to work without fear", insisting the East African country is safe for citizens and visitors.
Ogolla echoed the need to have hope for a better future and added: "The Kenyan people need a sustained commitment to peace, we cannot allow these events to derail that.
"Most of all we know that extremism thrives on hopelessness so above all we must continue to work together to offer hope for a brighter future to all the peoples of Kenya.
"Our thoughts and prayers are with the people affected by this horrific attack."
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