Republican senators opened the way for a new showdown with Barack Obama on Tuesday, after an apparently disastrous meeting with UN ambassador Susan Rice that had been widely seen as an attempt to smooth her path to nomination as US secretary of state.

The meeting on Capitol Hill had been expected to end in rapprochement after one of Rice's leading Senate critics, John McCain, stepped back from a bitter row over the 11 September attack on the US consulate in Benghazi.

But McCain and his colleagues emerged from the 90-minute private encounter to say they were "significantly troubled" by Rice's explanation of her earlier accounts of the attack on the US mission.

Four Americans died in the attack on 11 September, including the US ambassador to Libya, Chris Stephens. Five days after the incident, the White House put forward Rice to appear on the weekend talk shows in the US to give an explanation for what happened. Rice said the attack occurred after a spontaneous protest against an anti-Muslim film that had been produced in the US. The White House later said the Benghazi incident was a terrorist attack.

At the meeting with senators on Tuesday, Rice said her earlier version had been based on "incorrect" talking points given to her by the intelligence services.

Rice, who is reported to be Obama's favoured choice to replace Hillary Clinton at the State Department, insisted she had not intended to mislead the public. She told the senators that when she said on television that al-Qaida had been defeated, she meant that its core had been defeated.

McCain, who appeared to be even more irritated with Rice than before the meeting, was blunt. "We are significantly troubled by many of the answers that we got and some that we didn't get. It is clear the information that [Rice] gave the American people was incorrect when she said it was a spontaneous demonstration triggered by a hateful video. It was not, and there was compelling evidence at the time that that was certainly not the case."

One of McCain's colleagues, Lindsey Graham, said: "Bottom line, I'm more disturbed now than I was before [by] the 16 September explanation about how four Americans died in Benghazi."

Graham added: "If you don't know what happened, just say you don't know what happened. The American people got bad information on 16 September. They got bad information from President Obama, and the question is: should they have been giving the information at all?"

US ambassador Susan Rice. Photograph: Spencer Platt/Getty Images

The row is ostensibly over the round of television interviews Rice gave on the Sunday after the attack, when she played down the involvement of al-Qaida elements. Her interviews were at odds with the CIA, which said later it had been convinced from early on that an al-Qaida related group had been behind the attack.

Republicans argue that Rice, with one eye on the forthcoming presidential election, wanted to diminish the alleged role of al-Qaida because Obama had been claiming it had been defeated. But some leading figures in the GOP, including McCain, are still sore about how Democrats for months held up the appointment of John Bolton as UN ambassador in 2005. President George Bush eventually bypassed Congress to appoint him.

Jay Carney, the White House spokesman, accused Republicans on Tuesday of having an "obsession" over what Rice said. Carney said there were "no unanswered questions about Rice's appearance on the Sunday shows and the talking points that she used that were provided by the intelligence community. Those questions have been answered."

Obama has not yet said who he will nominate to replace Clinton after his inauguration on 21 January, but Rice has emerged as a favourite for what is the biggest job in the cabinet. Carney described her Tuesday as being "enormously qualified", without specifying a particular job.

The president was widely criticised in his first term of failing to stand up to Republicans in Congress, and he needs the psychological boost of early wins over the GOP if he is to hold out any hope of getting through significant legislation in his second term.

The combination of the Rice row and the showdown over taxes and spending offer the president an early opportunity to demonstrate he is going to be tougher in his second term.

Republicans do not have enough votes in the Senate to block a Rice nomination, but they could delay it for months through filibusters. Clinton has offered to remain in place until a successor has been appointed.

In her statement after meeting the senators on Tuesday, Rice admitted her talking points were wrong and there had been no protest or demonstration in Benghazi.

Rice, who was accompanied to Capitol Hill by the acting CIA director Michael Morell, said: "In the course of the meeting, we explained that the talking points provided by the intelligence community, and the initial assessment upon which they were based, were incorrect in a key respect: there was no protest or demonstration in Benghazi.

"While we certainly wish that we had had perfect information just days after the terrorist attack, as is often the case, the intelligence assessment has evolved. We stressed that neither I nor anyone else in the administration intended to mislead the American people at any stage in this process, and the administration updated Congress and the American people as our assessments evolved."

Rice, battling to keep her hopes of the secretary of state job alive, has further meetings scheduled with critical Republicans in Congress on Wednesday and in the coming weeks.

One of the Republicans at Tuesday's meeting, Kelly Ayotte, hinted she would try to block Rice's nomination if Obama chooses her. "I would place a hold on anybody who wanted to be promoted for any job who had a role in the Benghazi situation," Ayotte said.

Rice and senator John Kerry, who heads the Senate foreign affairs committee, are the two main contenders to replace Clinton. Rice has a reputation in the diplomatic community for being abrasive but has the backing of the first lady, Michelle Obama, and senior White House adviser Valerie Jarrett.