The 25-year-old Police Service Northern Ireland (PSNI) officer was killed when a bomb under his vehicle exploded on Saturday afternoon, just before 4 pm BST.
Paterson described the murder as "revolting and cowardly".
"It was carried out by those intent on defying the will of the people," Paterson told the House of Commons.
"These terrorists will not destabilise the peace process. The Omagh bomb in 1998 did not, and nor can this."
"They failed then and they will fail now," he added.
"The PSNI have support from right across the community.
"This was evident when the first and deputy first ministers stood shoulder to shoulder with the justice minister and the chief constable to call for active support for the PSNI.
"They now have begun the painstaking task of carrying out the murder inquiry and will not stop until those who are intent on evil are brought to justice."
During a press conference on Monday, Detective Superintendent Raymond Murray said that the bomb which killed Kerr was probably up to one pound in weight.
It had been placed inside a plastic lunch box, which had been attached under the victims car.
Det Supt Murray said the device was probably detonated by a tilt switch, which is set off by movement. Some components of the bomb had been recovered from the scene.
Police believe it was planted some time between Thursday evening and Saturday afternoon, when it detonated.
Constable Kerr killed outside his home in the Highfield estate in Omagh, County Tyrone. Kerr, joined the police force in May 2010 and had been working in the locality since December.
His mother Nuala has since urged Catholics not to be discouraged from joining the PSNI.
Speaking about the murder Cardinal Archbishop Sean Brady described it as an attack on all of society.
"I call on young Catholics to actively support the PSNI and join it. We need a police force that represents all of us.
"I also appeal to the parents of children that are being recruited by these groups to get their children to resist," he said.
"They have not lived through the dark days of the Troubles, tell them the awfulness of what we lived through."
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