Scott Morrison has pledged to govern “humbly” in the next term of parliament, crediting hardworking Australians who “want to get ahead” for the Coalition’s surprise victory.

Welcoming new MPs and senators to the Coalition party room in Canberra for the first time since the 18 May election, the prime minister said MPs and senators would “burn for the Australian people every single day”.

“This was a victory for the Australian people and it is our job to govern humbly for this nation, to have them very much at the centre of our thoughts each and every day,” Morrison said.

“When we focus on the Australian people that makes our government stronger.”

Morrison also told MPs that the Coalition was well placed to score further seat gains at the next election, saying the party will continue to work in Labor-held electorates to build its vote, while warning of the “wasteland” of opposition.

“There are many other areas of Australia (where) we should be able to build the Coalition vote and secure future victories,” he told MPs, including 28 new members of the party room.

Acknowledging “quiet” Australians for the victory that has the Coalition on track to secure a majority of at least 77 seats in the House of Representatives, Morrison praised hardworking Australians studying and working for the government’s reelection, singling out small business owners and farmers.

“This was a victory for Australians that just want to work hard and get ahead; this was a victory for those who put in that effort.

“By keeping our focus on them, and as we engage the issues and challenges which our nation faces – which are significant – whether it is the economy or national security or the environment or elsewhere, if we keep our focus on them we will always stay true to the values we hold dear as Liberals and Nationals in this party room.”

After welcoming the new MPs and senators, Morrison praised the Nationals leader, Michael McCormack, the Liberal deputy leader, Josh Frydenberg, the Senate leader, Mathias Cormann, and the work of the Coalition’s campaign headquarters, including the party director, Andrew Hirst.

The new members for Herbert, Phillip Thompson, left, and Wentworth, Dave Sharma, are welcomed to the Liberal party room. Photograph: Mike Bowers/The Guardian

Saying the Coalition would have a singular focus on economic management to ensure it could provide the services Australians rely upon, including action on climate change and youth suicide, Morrison said he had a “simple task” ahead.

“Here we are a fresh team, a team that is hungry, a team that is committed, a team that is united in the way that we were able to fight in this campaign to do one very simple thing – and that is to ensure that Australians will be at the centre of our gaze,” he said.

“We will govern with humility, we will govern with compassion, we will govern with strength and we will govern for all Australians.”

While the date for the first week of the 46th parliament still depends on when the Australian Electoral Commission returns the writs, Morrison told his MPs he expected that they would return in the first week of July.

Passing income tax cuts is the government’s first order of business, with the Coalition likely needing the support of crossbench senators to legislate the reform.

The party room meeting comes after Morrison unveiled a revamped frontbench on Sunday that dumped the former environment minister Melissa Price from the cabinet, replacing her with Sussan Ley.

In a warning to the new executive that other talented MPs were waiting in the wings for promotion, Morrison said he expected his new ministry to perform.

“There is a wealth of talent in the government party room which will keep the pressure to perform on all of us,” he said.

Some Nationals have expressed unhappiness with the reshuffle, which saw its quota of ministerial positions reduce from five to four, with the portfolio of water and agriculture split between two Nationals.

Morrison has also made way for two cabinet vacancies by appointing Arthur Sinodinos as the new US ambassador and Mitch Fifield as the ambassador to the United Nations.

Morrison’s first party room meeting comes as Labor’s new leader, Anthony Albanese, travels to Queensland to try to reconnect with voters who abandoned the party in the state.