David Cameron has defended his plan to carry out billions of pounds of extra cuts to benefits for the working poor, saying it is only fair to ensure welfare payments are not rising faster than earnings.

The prime minister insisted the proposals for £3bn-a-year cuts, set out by the chancellor, George Osborne, on Monday, were better than raising taxes or reducing benefits for wealthier pensioners. The plan means a two-year freeze on benefits and tax credits for about 10m households, many of whom have already borne the brunt of austerity.

However, in a round of broadcast interviews, Cameron claimed voters would give the party credit for “levelling” with the electorate about forthcoming welfare cuts under a Conservative government.

Asked how he would respond to people who felt the cuts were falling unfairly, he said: “What I would say to them is that we are and we will continue to cut your taxes and that’s the best way to help the hard-working families that are in work. You can now earn up to £10,000 before you pay income tax, it will be £10,500 next April and that has taken 3 million people, 3 million of the lowest paid out of income tax altogether. Now, it’s not an easy thing to do but I think we owe it to the British public to explain how we’re going to raise this money.”

He insisted that the move was fair. “What this will mean is that between 2007 and 2017, benefits would have been going up at about the same speed as earnings and, frankly, is it really fair to say to people: your benefits are going to go up faster than the earnings of people whose taxes pay for your benefits? I don’t think it is fair and that’s why I think what George did yesterday was a difficult choice but the right one.”

Pressed on why wealthier pensioners were being spared economic pain once again, the prime minister said: “The choice that we have made [is] saying if you have worked hard and saved and you’re in retirement, you deserve dignity and security, so we have protected the basic state pension, which is up £15 a week since I became prime minister. I don’t think pensioners should be asked to bear the burden.”

The Conservatives appear to have taken a calculated political gamble by spurning the chance to ease austerity. The chancellor’s move, which will cut £3bn a year from the welfare budget, is designed to cement the Conservatives’ reputation as the party willing to take tough long-term economic decisions, even at the cost of hitting more than 5 million families characterised as working poor.

The freeze will hit the poorest third in society the hardest and cause working families with children lose as much as £490 a year in child benefit and tax credits. The average loss will be £300 a year per household but it will vary greatly.

Resisting the temptation to offer a traditional pre-election bribe, Osborne also announced that he was continuing with a freeze on public sector pay until 2017, meaning public sector workers will have seen their pay held back below inflation for seven years.

In his speech to the Conservative party conference in Birmingham, Osborne said he was levelling with the British people that now was not the time to ease up on cutting the deficit. “The problem for Britain is not that it taxes too little – it spends too much.”

Conservative strategists made the calculation that candour about the difficult spending choices ahead will gain Osborne political kudos and outweighs the risk of reinforcing a reputation for putting the burden of deficit reduction on to the backs of the poor. But there was a nervousness among some senior Tories that Osborne had abandoned the last vestige of compassionate Conservatism and bet the farm on such an unflinching approach to the deficit.

“And I tell you in all candour that the option of taxing your way out of the deficit no longer exists if it ever did,” the chancellor said.

Osborne balanced the tough message by announcing he was going to tackle technology companies such as Apple and Google, which have been accused of going to extraordinary lengths to secure offshore profits to avoid corporation tax. Apple’s tax deals will come under further scrutiny this week amid a threat that the EU will impose a multibillion-pound fine this week for its decades-long deals with the Irish government.

Tory officials said detailed measures would be announced in the autumn statement, but hundreds of millions of pounds would be saved from the multinational clampdown on corporate tax avoidance. The two-year working-age benefits freeze takes £3.2bn a year off the welfare bill by 2017-18, the first step of the chancellor’s commitment to wipe £12bn more from the annual welfare bill.

This leaves Osborne still to find a further £9bn in welfare cuts in the first two years of the next parliament. Osborne also said he would slash general departmental spending by a further £13bn in the first two years of the parliament – enough, alongside growth, to put the overall budget in surplus by 2018. He said the latest Treasury estimate calculated £25bn was needed overall to eliminate the deficit, a figure that some government sources said might be an underestimate.

After the speech, Osborne’s aides tried to flush out how quickly the shadow chancellor, Ed Balls, would cut the deficit if he would not match Osborne’s welfare cuts.

But Labour stressed it would make different choices, including raising taxes on the wealthiest. Osborne also took aim at the Labour leader’s failure to mention the deficit: “Did you hear that speech last week? Ed Miliband made a pitch for office that was so forgettable he forgot it himself. Well, I have to tell you in all seriousness that forgetting to talk about the deficit is not just some hapless mistake of an accident-prone politician, it is completely and totally a disqualification for the high office he seeks.”

The chancellor’s proposals have caused tension in the coalition, with the Liberal Democrats indicating that they are opposed to the widespread benefits freeze. A Lib Dem source said: “We have consistently blocked Conservative attempts to freeze benefits for the working-age poor just as they have blocked our attempt to cut benefits for the wealthiest pensioners. It speaks volumes about the priorities of the Conservative party that they see benefit cuts for the working poor as a crowd-pleasing punchline for a conference speech.”

The detailed plan will see all the main working-age benefits, including child benefit, frozen at their post-election levels rather than being uprated in line with inflation.

Conservative officials said a working couple with one child, with each parent earning £13,000 a year, would lose £44 a year in child benefit and £310 a year in tax credits. A household with a single earner and two children would lose £75 a year in child benefit and £420 in tax credits. In 2012 Osborne imposed a 1% cap on most benefits, but the new proposed two-year total freeze for the first time includes housing benefit.

The officials justified the freeze by arguing that earnings have grown by 14% since 2007 while most working-age benefits have been uprated by 22.4%. Due to the two-year freeze and the 1% cap on increases announced in the autumn statement, the gap between earnings and working-age benefits would be eradicated by 2017, the sources said.

Osborne gave himself little political room for manoeuvre by, in effect, ruling out any tax rises to cut the deficit. He told delegates: “In a modern global economy where people can move their investment from one country to another at the touch of a button and companies can relocate jobs overnight, the economics of high taxation are a thing of the past.”

The chancellor also said he would seek to end youth unemployment by giving jobless 18- to 21-year-olds six months to find work or training before their jobseeker’s allowance would be withdrawn.