Prime Minister Tony Blair is still opposed to the death penalty, his official spokesman has insisted.
Pc Beshenivsky had three children and two step-children
Ex-Met Police chief Lord Stevens called for the death penalty to be reinstated for people who kill police, following the killing of Pc Sharon Beshenivsky.
But Mr Blair's official spokesman said the government's view was unchanged.
Shadow home secretary David Davis, who has personally backed the death penalty in the past, said it was not the "right atmosphere" to make such judgements.
Pc Beshenivsky was shot in Bradford when she answered a call to an armed robbery at a travel agency. Her colleague Pc Teresa Milburn, 37, was injured in the incident, but has since left hospital.
At the weekend Lord Stevens said in the News of the World that the "cold-blooded" murder of Pc Beshenivsky had "finally" changed his mind on the death penalty.
"Such an extreme act of pure evil can only be met by the most extreme of responses - and that can only be death," he told the paper.
However, the prime minister's official spokesman said: "The government's view is still against the death penalty - other people are entitled to their views."
Mr Davis, who has in the past called for the return of the death penalty for some pre-meditated and cold-blooded multiple murderers, told BBC Radio 4's Today programme that although he was an admirer of Lord Stevens, "on this, however, I do not think he is right".
"This is not the right circumstances to make these judgements," he said.
"It is clearly a very emotional time - everybody is very shocked and upset by the hideous killing and wounding of these two police officers.
"I am not at all sure that this is the right atmosphere in which to make such a judgement."
He said that if he became prime minister he would not try to reinstate the death penalty because it would not have the support of a majority of MPs.
He also warned that the worst thing about having the death penalty was making "a mistake".
Roger Knapman, leader of the UK Independence Party, said Britain could not reintroduce the death penalty because membership of the European Union precludes capital punishment.
"However horrific the crimes, there is no prospect of the death penalty being re-introduced in the UK unless we first leave the European Union." he said.
Mr Davis accused the government of failing to tackle the source of gun crime and particularly the illegal holding of firearms.
"One of the things that's very clear is the government is not doing enough in terms of its border control or inspection of imports, inspection of internet imports - the whole series of things which need to be done if we are going to bring this epidemic of gun crime under control."
He said gun crime had doubled to around 10-11,000 since 1996 when Thomas Hamilton killed 16 children and a teacher at Dunblane Primary School in Scotland.
Home Secretary Charles Clarke said the government was keen to learn any lessons from the Bradford shootings.
"My main priority is to ensure that guns no longer have a place on our streets and that armed gangs who terrorise innocent people are brought to justice," he said.
But he signalled his opposition to arming all police, citing evidence from other countries which suggested it encouraged criminals to carry guns.
"I remain sceptical that arming all police officers all of the time would make them safer," he said, writing in The Sun.
"Indeed, all the experience from other countries where the police carry firearms demonstrates that this only encourages the criminals to arm themselves and potentially to turn law enforcers' own weapons on to the police themselves."