Barack Obama has rejected the former US vice-president Dick Cheney's defence of waterboarding, citing the refusal of the then British prime minister, Winston Churchill, to resort to torture even at the height of the Blitz in the second world war.

At a White House press conference to mark his first 100 days in office, the president addressed issues ranging from concern over Pakistan's nuclear arsenal falling into militant hands to Bush administration torture policies.

Obama said he was comfortable with his decision to ban waterboarding and other harsh interrogation techiques used at Guantánamo Bay and Central Intelligence Agency (CIA) secret detention centres around the world under his predecessor George Bush.

In an unequivocal statement, he said: "I believe that waterboarding was torture and, whatever legal rationals were used, it was a mistake."

Obama has been criticised, in particular by Cheney, for making public four secret Bush administration memos detailing interrogation techniques approved for use by the CIA, including waterboarding. Cheney has called on Obama to release other classified documents he claimed would show that valuable intelligence was gained from detainees interrogated in this way.

Obama responded by pointing to the example from the Blitz: "I was struck by an article that I was reading the other day talking about the fact that the British, during world war two, when London was being bombed to smithereens, had 200 or so detainees. And Churchill said 'we don't torture', when all of the British people were being subjected to unimaginable risk and threat. And the reason was that Churchill understood you start taking shortcuts, and over time, that corrodes what's best in a people. It corrodes the character of a country."

Obama said he had read the classified material mentioned by Cheney, but this did not answer the question of whether the information could have been obtained in another way and whether use of these techniques made the US safer.

Obama said he believed it was possible to get information in ways that stayed true to the country's ideals. Torture had provided al-Qaida with a recruiting tool, he added.

He promised to try to be more open about sensitive documents that are classified or released with large parts blacked out. There were times when the national interest dictated such an approach, but it was a blunt instrument, he said. His administration was looking into alternative mechanisms, such as a judge being given access to classified material to make a ruling.

Asked about US worries about Pakistan and whether its nuclear arsenal might fall into militant hands, Obama said he was "gravely concerned" about the fragility of Pakistan. But he added: "I'm confident that we can make sure that Pakistan's nuclear arsenal is secure, primarily, initially, because the Pakistani army, I think, recognises the hazards of those weapons falling into the wrong hands.

"We've got strong military-to-military consultation and cooperation. I am gravely concerned about the situation in Pakistan, not because I think that they're immediately going to be overrun and the Taliban would take over in Pakistan; more concerned that the civilian government there right now is very fragile."

He was concerned too, but not to the same degree, about the recent resurgence of violence in Iraq. "The political system is holding and functioning in Iraq" and the incidence of bombings "remain very low relative to what was going on last year".

He was speaking at the end of a day in which he celebrated the 100 days milestone with a joint appearance at the White House in the morning with the Democratic party's newest recruit, Arlen Specter, the Republican senator, who could potentially give the Democrats a filibuster-proof majority in the Senate.

He had another cause for celebration later in the day when both the House and the Senate voted in favour of his $3.4tn budget, the biggest spending bill in US history. Not a single Republican in either chamber voted for it – and neither did the Republican defector Specter.

The budget is one of the most redistibutive in recent US history, with measures that include putting aside cash for the creation of a nationwide healthcare system.

After a flight to the midwest to address a townhall-style meeting at Arnold, near St Louis, Missouri, Obama held his third televised press conference since taking office.

At the press conference, he expressed satisfaction with the way the first 100 days had gone and tested out a slogan for his era, the New Foundation, echoing the New Deal. But it seems likely to fall by the wayside, as have other slogans the Obama administration has tested.

Obama, a smooth talker when reading from a teleprompter, is frequently thrown by the impromptu nature of press conferences and appeared stuck when asked what had surprised, troubled, enchanted and humbled him in his first 100 days in office. He said he had been surprised by the convergence of so many crises. Most presidents had only to deal with two or three at the same time whereas he faced seven or eight, he said.

He was troubled by the lack of cooperation from the Republicans and, strugging to find an answer, said he was "enchanted" by those serving in the US military, although he admitted enchanted was not quite the right word.

And he was humbled by the limits on his power, a recognition that there were other power bases in the country such as bankers and Congress that did not do what he wanted.

Today, he wakes up with another 1,362 days of his first term still to go.