Police have asked the government for a new counter-terrorism power to stop and search people without having to suspect them of involvement in crime, the Guardian has learned.

Senior officers have told the government the new law is needed to better protect the public against attempted attacks on large numbers of people, and are hopeful they can win ministers' backing.

A previous law allowing counter-terrorism stops without suspicion, section 44 of the Terrorism Act 2000, was scrapped this year by the home secretary, Theresa May, after European judges struck it down for breaching human rights.

But police, including the Metropolitan force, which leads the UK fight against terrorism, say they need a boost to their counter-terrorism powers, which they worry are now too weak.

They have asked for a law which would be much more limited than section 44. It would be restricted to a specific period of time and to a limited geographic area or a specific place or event.

The new stop and search power would need primary legislation to become law and it is believed it could be introduced within months. Police believe it will be needed to protect events such as the 2012 Olympics in London, state occasions such as trooping the colour, and major summits such as the G20 when they are held in the UK.

Stop and search powers are controversial because ethnic minority people have been targeted more than white people, triggering claims that some officers are using them in a discriminatory way.

A source with knowledge of the discussions told the Guardian: "The key thing is to get this power without its use being random. You can't have a random power because of the judgment, but some new power is needed. The power would need to be signed off by a senior officer, maybe even a chief constable, and the home secretary. It could cover an event of high importance such as the Olympics. It would be for a limited time and in a limited geographical place, and at a time when the threat level is severe."

Currently section 43 of the Terrorism Act allows searches, but an officer must have reasonable suspicion for the stop to be lawful. The source added that police were now tactically hampered in the fight against terrorism.

Another source with knowledge of the plans said: "Everyone now realises it [section 44] was a blunt instrument. If it is time-limited, it should comply with the European ruling."

The issue of powers to fight terrorism that infringe on civil liberties is causing friction within the Conservative-Liberal Democrat coalition. A review of counter-terrorism powers has already been delayed after a row over whether control orders should be retained.

Section 44 fell into disrepute because it is believed that it failed to lead to the capture of a single terrorist, and it was used in some cases against protesters and photographers. It was struck down by the European court of human rights after a case brought by Liberty, the civil liberties pressure group.

In that case, police had used the counter-terrorism power against a peace protester, Kevin Gillan, and a journalist, Pennie Quinton, as they travelled to a demonstration outside the annual arms fair at the ExCel centre in east London in 2003.

The crucial aspect of the ruling, and thus the hurdle any new power must clear, is not to be random and indiscriminate in its scope. Shami Chakrabarti, director of Liberty, said that with the right safeguards her organisation might not oppose the new power: "The devil will be in the detail. What safeguards will there be, who can trigger the power, what is the threshold for turning it on, what public scrutiny will there be?"

Under the old power all of London was designated for months on end as a place where police could stop people without suspicion. Chakrabarti said: "The geographical area can't be an entire county or all of London as it was before, but an area no greater than a square mile. It must not be for months on end but for a specific period of 24 to 48 hours.

"It must target specific places, not classes of people, on the basis of intelligence and risk for narrow windows of time, with adequate authorisation and transparency. Then it will satisfy proportionality and equal treatment whilst providing a rational, flexible aid to anti-terror policing."

Ben Bowling, a professor of criminology at King's College London and founder member of Stopwatch, which campaigns against alleged police abuses of stop and search powers, warned the new power could be used to discriminate against ethnic minority Britons: "Where officers have the maximum discretion, that is where you have the greatest racial discrimination in the way police have used their powers. We would want to be absolutely certain that police are not targeting ethnic minority communities for unfair stops and searches."

The debate about the proposed new power will be shaped by the memory of section 44. Some police leaders now accept they were too slow to realise the damage it was doing to community relations and to their own reputation, while proving of questionable value in catching terrorists. In 2009 more than 100,000 stops were carried out under section 44, but not a single arrest was made for terrorism under the power.

Britain is facing a double terror threat for the first time in a decade. Counter-terrorism officials believe the risk of attack from al-Qaida-inspired violent extremists is "severe".

But added to that, officials assess as "substantial" the risk of an attack on the mainland by dissident republican terrorists. That is one level lower than the threat posed by Islamist violence. Northern Ireland has this year been hit by repeated terrorist attacks and attempted attacks, one source said, as the capability of dissident republican terrorists grows.