The government needs to reflect and do more, Culture Secretary Lucy Frazer has said following bruising losses for her party in local elections in England.
Some Conservatives have blamed Rishi Sunak after the party lost more than 1,000 councillors in Thursday's vote.
But, speaking to the BBC, Ms Frazer said that, despite a difficult start to the Tories' campaign, voters "were beginning to give Rishi Sunak credit".
Labour's Wes Streeting said the "best is yet to come" for his party.
Speaking to the Sunday with Laura Kuenssberg programme, the shadow health secretary said he was "confident Labour can win a majority in the next election, but not complacent... we're not taking people for granted".
The party won control of 22 councils including crucial battlegrounds such as Medway, Swindon, Plymouth, Stoke-on-Trent, and East Staffordshire.
Pressed on whether the party had made enough progress to form the next government, Mr Streeting argued people who voted for small parties in these local elections, would switch to Labour in the next general election, expected in 2024.
Despite winning in key areas, some have suggested their vote share, if repeated in the general election, could leave Labour short of an overall majority, and dependent on joining up with other parties to form a government.
Mr Streeting did not rule out forming a coalition with the Liberal Democrats, saying Labour was "just not in the ball park of talking about coalition governments".
He also said that changing the voting system by introducing proportional representation would not be in the Labour manifesto - traditionally, that has been seen as the price to pay to get the backing of the Liberal Democrats in case of a hung Parliament.
Speaking to the same programme, Liberal Democrat leader Sir Ed Davey - who also enjoyed a positive set of results on Thursday - ruled out going into a coalition with the Conservatives, but refused to do the same for Labour.
He said it was a "hypothetical question" adding that he would not "take the voters for granted".
Reflecting on the possibility of a hung Parliament at the next election, the SNP have said their MPs could hold the balance of power.
SNP Westminster deputy leader Mhairi Black said "a strong team of SNP MPs would put Scotland in the driving seat of a minority UK government" adding: "With Keir Starmer's pro-Brexit party becoming increasingly indistinguishable from the Tories, the SNP would drag the Labour Party to the left."
Laura Kuenssberg explains that Labour hopes the party will build so much support in the next year that a conversation about coalition will be irrelevant - and the Conservatives would like to stir up a debate about the issue.
Asked if the Conservative government would change following the party's poor performance, Ms Frazer said "we absolutely need to reflect" but argued voters would regain trust in the party once "people see us delivering".
She said Rishi Sunak had only been prime minister for six months but the public were "slowly beginning to give the government and Rishi credit".
She also said the results needed to be seen in the context of the pandemic and the war in Ukraine, which she said had affected the cost of living crisis.
However, the local election results have prompted some Conservatives to question the government's direction, both privately and publicly.
Veteran party MP Sir John Redwood tweeted: "Last Thursday many Conservative voters went on strike. They do not want to vote for higher taxes, anti enterprise policies and a failure to take back control of our borders."
The Conservatives lost votes to Labour and the Liberal Democrats, but also to the Greens, who achieved their best-ever result in local elections gaining the party's first majority on an English council, in Mid-Suffolk.