In Londonderry, Inspector John Burrows said everyone in the police service appreciated the public's support.
"We are massively grateful for the people of Derry who've turned out to support the police," he said.
"They have come to show solidarity, I believe, with the police and to send a very clear message out to the people who killed Constable Stephen Carroll and the two soldiers that they do not represent them."
Prime Minister Gordon Brown has sent words of support to MPs who held a vigil outside Westminster in support of the peace rallies held in Northern Ireland.
Conservative MP Sir Patrick Cormack, chairman of the Northern Ireland Affairs committee, said the demonstration at Westminster showed "our resolve to stand with the people against violence".
"We have been deeply moved by what has happened this week, but we were totally revolted by the appalling murders, but out of that tragedy a new strength has come," he said.
In Dublin, Taoiseach Brian Cowen said those who carried out the attacks were a "tiny and unrepresentative group of evil people who have no mandate and no support for their actions".
Pope Benedict XVI has added his voice to the condemnation, calling the murders "abominable acts of terrorism".
A reward of £100,000 for information leading to the arrest and conviction of the killers of Constable Carroll and two soldiers has been offered by the Sun newspaper in conjunction with the Crimestoppers charity.
Dissident republican group, the Continuity IRA, said it shot Constable Carroll at Lismore Manor, in Craigavon, on Monday.
On Saturday, sappers Mark Quinsey, 23, from Birmingham, and Patrick Azimkar, 21, from London, were shot at Massereene Army base, Antrim.
The Real IRA said they killed the soldiers, who died in a hail of bullets as they accepted a pizza delivery at about 2120 GMT.
Four men were also injured in the attack. One of them is in a critical condition and another is seriously ill.
A youth aged 17 and a 37-year-old man remain in police custody for questioning in connection with the murder of Constable Carroll.
There were minor disturbances in Craigavon on Tuesday night, where wheeled bins were set on fire after the police raids.
Meanwhile, serving and former police officers due to give evidence to the Robert Hamill inquiry have been granted temporary anonymity.
The ruling was made following Constable Carroll's murder and what the inquiry chairman said was the "increased security threat" to police officers in Northern Ireland.
Police chiefs from Northern Ireland and the Irish Republic are to meet on Thursday to assess the security threat posed by dissident republicans.
Chief Constable Sir Hugh Orde and Garda Siochána Commissoner Fachtna Murphy will meet in Belfast.
British and Irish ministers met for a security summit at Hillsborough Castle in County Down on Tuesday, where they pledged the attacks would not be allowed to derail the peace process.
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