Former PM Liz Truss had thrown doubt on the aim, saying she wanted to scrap "Stalinist" housing targets.
But Mr Gove - who returned to cabinet after Ms Truss's resignation - told the BBC he wanted to build more homes, both for ownership and to rent.
He added that new developments should have the consent of local communities.
The minister also warned meeting the target would be "difficult" due to the economic circumstances.
"We need to be straight with people: the cost of materials has increased because of the problems with global supply chains and also a very tight labour market means that the capacity to build those homes at the rate we want is constrained," he said.
Asked about Ms Truss's past comments on housing targets, Mr Gove said: "The top-down housing targets that... Liz was referring to are part of a broader and different calculation from the 300,000 in the manifesto.
"My view is that what we do need is a fair way of allocating housing need that takes account of changes in population."
He said new developments should be "more beautiful", have the consent of the local community, be accompanied by the right infrastructure and protect the environment.
During the interview on Sunday with Laura Kuenssberg, Mr Gove also avoided saying whether the government would raise benefits in line with inflation.
He said there would be "tough decisions" but that the prime minister's "instinct" was to help the vulnerable.
Speaking to the same programme, former Conservative Chancellor Philip Hammond - who originally set the target - said he would be "very surprised" if the government did not increase benefits in line with inflation.
The UK is experiencing what many have described as a housing crisis, with millions living in sub-standard conditions and long waiting lists for council houses.
However, building more homes has proved a headache for Conservative prime ministers.
In 2017, then-chancellor Mr Hammond set the target of building 300,000 homes a year by the mid-2020s and the party recommitted to the aim in its 2019 manifesto.
However, Boris Johnson's efforts as prime minister to increase building by forcing local councils to accept new housing developments in certain areas had to be paused after a backlash from his own MPs, one of whom warned it would see the south of England "concreted over".
Earlier this year, former housing secretary Robert Jenrick said the government would "miss their 300,000-homes-a-year manifesto pledge by a country mile".
In the Conservative leadership campaign over the summer, Ms Truss hinted she would scrap the target, telling The Telegraph "I want to abolish the top-down Whitehall-inspired Stalinist housing targets - I think that's the wrong way to generate economic growth."
During the contest, Mr Sunak's team also said he did not believe in arbitrary or top-down numbers for housing.
In May, Mr Gove himself appeared to cast doubt on the target.
He said the government would do all it could to meet the figure, but added that it would be "no kind of success simply to hit a target if the homes built are shoddy, in the wrong place, don't have the infrastructure and are not contributing to beautiful communities".
"Arithmetic is important, but so is beauty, so is belonging, so is democracy," he had said.
However, when asked by Laura Kuenssberg if the government was still committed to the 300,000 figure, Mr Gove said: "Yes."
He also confirmed that he would be continuing with previously announced legislation to tackle rogue landlords, saying: "These chancers are leaving people in dire circumstances."