Voters believe Boris Johnson is decisive and strong but also dishonest and out of touch, a poll has revealed.
It comes after a weekend in which hundreds of thousands of people marched through the streets of the UK in protest at his plan to suspend Parliament.
Mr Johnson has warned Tory rebel MPs they will be sacked if they go against the government and try to block a no-deal Brexit in the Commons this week.
The YouGov survey of 1,867 adults for The Times newspaper found that the prime minister has improved his public reputation in his first month in Number 10.
In a poll taken on August 29, 62% of voters said Mr Johnson is “decisive”, an increase from 38% when surveyed on July 22.
More than half of voters - 52% - said he was strong, compared to 41% a month earlier.
And four out of ten people believe Mr Johnson is a competent leader, up from 29% in July.
However, the poll found that still more than half of people believe Mr Johnson is untrustworthy, dishonest and out of touch.
A total of 53% said he was untrustworthy, a decrease from 58% when he became prime minister.
In addition, almost half - 49% - said he was “putting on an act”.
The poll found that only 7% of Remainers found Mr Johnson to be honest.
Meanwhile, Mr Johnson was accused of "goading" some Tory MPs to rebel so he can force a snap general election having purged opponents of a no-deal Brexit from the party.
Former Conservative justice secretary and rebel ringleader David Gauke accused the prime minister of deliberately trying to lose votes to block a deal-less departure this week.
Mr Johnson has put rebels within his party on notice that they face losing the whip and being barred from standing for the Tories if they vote against the government.
Mr Gauke said: "I don't think there seems to be a huge effort to persuade people to support the government this week.
“I think they seem to be quite prepared for there to be a rebellion, then to purge those who support the rebellion from the party.
"None of that is happening. The usual operation isn't particularly happening. It does seem to me they are almost goading people into voting against the government.
"Because I think the strategy, to be honest, is to lose this week and then seek a general election having removed those of us who are not against Brexit, not against leaving the European Union, but believe we should do so with a deal."