Boris Johnson is trying to focus attention on tackling crime and recovering from the coronavirus, despite a number of allegations against him that may damage his party’s election chances.
Two new polls suggest the Conservative lead over Labour has been trimmed ahead of Thursday’s local elections in England and voting for parliaments in Scotland and Wales.
In The Mail On Sunday, the prime minister said he would "bring the hammer down hard on the gangs" and set up a "pet theft task force" as part of plan to get tough on crime.
He added: "If we are to succeed in levelling up across the UK, we must give everyone the security and confidence that comes from having a safe street and a safe home."
He also praised the COVID-19 vaccine programme, saying: "This country is moving forwards cautiously but I hope irreversibly through the steps of the roadmap.
"Week after week we are seeing how the vaccine rollout is helping to restore our freedoms – and with those freedoms I have absolutely no doubt that our economy will bounce back strongly."
An Opinium poll last week showed the Conservatives falling to a five-point lead over Labour, with 42% compared to 37%.
It is a two-point fall for the Tories and a four-point improvement for Labour compared to a week earlier.
A Focaldata poll put Labour on 39%, one point behind the Tories.
The polls come as concerns grow within the party that recent "sleaze" claims against Mr Johnson will be costly at the ballot box.
The Electoral Commission is investigating whether any donations or loans to pay for the refurbishment of his Downing Street flat were properly declared.
And he has denied saying he would rather see "bodies pile high" than impose a third coronavirus lockdown.
Also, a new claim emerged in The Sunday Times that an MP received a complaint from a Tory donor saying they were asked to pay for a nanny for the prime minister’s one-year-old son Wilfred.
The donor was alleged to have said: "I don’t mind paying for leaflets but I resent being asked to pay to literally wipe the prime minister’s baby’s bottom."
A Number 10 spokeswoman said: "The prime minister has covered the cost of all childcare."
But she did not respond when asked if Mr Johnson paid for the original bill himself or had reimbursed somebody else.
Mr Johnson has denied breaking any laws over the refurbishment of his official residence and insists he paid "personally" for the work.
But he has refused to say whether he received an initial loan from his party.
Earlier, former aide Dominic Cummings accused Mr Johnson of wanting donors to "secretly pay" for the work in a "possibly illegal" move.