Mr Gleeson pointed to recent efforts to bring down prices for shoppers, including the introduction of an Aldi and Lidl price match scheme earlier this year, while investing £70m in lowering prices.
At the same time, bosses have been working to disentangle its IT systems inherited from its former owner Walmart.
It was bought by the billionaire Issa brothers Mohsin and Zuber Issa and private equity firm TDR Capital for £6.8bn in 2021.
Mr Gleeson said: “We have achieved a huge amount in the first half of the year – it’s not been without its bumps along the way.
“I think it’s right to make sure that as we face into the second half of the year and the completion of that programme, that we invest in stores, invest in replenishment, to ensure we maintain and improve availability going into that important period in the lead into Christmas.”
He added that recent issues with Asda’s payroll system, which saw around 10,000 workers receive incorrect payslips, had now been fixed.